f(x)=√x
Find the derivative using the definition of derivatives

Answers

Answer 1

The derivative of the given expression is as follows   = [tex]\frac{1}{2 \sqrt{x_0}}[/tex]

definition of derivatives:

The derivative is the rate of change in a function without respect to a variable in mathematics. Derivatives are essential for solving calculus as well as differential equations problems.

What is a derivative and what are the many types?

Options, forwards, futures, and swaps are the four primary types of derivative contracts. Options represent derivative contracts that provide the buyer the right to buy or sell the underlying asset at a predetermined price during a specific time period. The purchaser is not required to execute the option.

According to the given data:

Let f:(0,∞)→R;

f(x)=√x, and x₀∈(0,∞) be an accumulation point of (0,∞).

We must find f′ such that for all x₀, f′(x₀) defined as:

limx→x₀(f(x)−f(x₀))/(x−x₀) exists.

Now,

x−x₀=(√x−√(x₀))(√x +√(x₀)).

Then:

[tex]\lim _{x \rightarrow x_0} \frac{f(x)-f\left(x_0\right)}{x-x_0}[/tex] = [tex]\lim _{x \rightarrow x_0} \frac{\sqrt{x}-\sqrt{x_0}}{\left(\sqrt{x}-\sqrt{x_0}\right)\left(\sqrt{x}+\sqrt{x_0}\right)}[/tex]

                            = [tex]\lim _{x \rightarrow x_0} \frac{1}{\sqrt{x}+\sqrt{x_0}}[/tex]

                            = [tex]\frac{1}{2 \sqrt{x_0}}[/tex]

The derivative of the given expression is as follows   = [tex]\frac{1}{2 \sqrt{x_0}}[/tex]

To know more about derivative visit:

https://brainly.com/question/25120629

#SPJ9

The question you are looking for is:

Use the definition to find the derivative of f(x)=(√x), for x>0. Is f differentiable at zero? Explain.


Related Questions

A parking lot is shaped like a parallelogram and bounded on four sides by streets, as shown in the figure to the right. How much asphalt (in square yards) is needed to pave the parking lot?

The amount of asphalt needed to pave the parking lot is __ yd^3, yd, or yd^2 ​

Answers

Amount of Asphalt needed =  27000 square yards

The shape of the parking lot is a parallelogram.

In the figure, the base of the parking lot is of length 180 yd and the height of the parking lot is 150 yd.

If 'b' is the base of the parallelogram and 'h' its height, then area of the parallelogram, A = bh

So here, base length, b = 180 yd

and height, h = 150 yd.

Therefore, area of the parking lot which is parallelogram, A = bh

                                                                                                   =  180 x 150

                                                                                                   = 27000 yd² (square yards)  

Amount of Asphalt needed to pave the parking lot = Area of the parking lot

                                                                                      = 27000 square yards  

Learn more about area of parallelogram at https://brainly.com/question/24291122

#SPJ1

Help please .
I can’t figure out magnitude . Can anyone help me ASAP ?

Answers

Answer:

|-20|    |12.3|     |8|     |-6|    |-4|     |2 3/10|      

Step-by-step explanation:

Magnitude in this context means that they want you to order the values from greatest to least.  These are all absolute values and that means distance from zero without regard to sign.  So if you just stripped the signs and absolute value symbols off of each value, then ordered them from largest to smallest, and THEN added the signs and absolute value symbols back, you have the answer.

Answer:

From greatest to least magnitude

|-20|

|12.3|

|8|

|-6|

|-4|

[tex]\lvert {2 \frac{3}{10}}\rvert[/tex]

Step-by-step explanation:

The absolute value of a number |x| is the positive value of x. So if x is positive then it's the number itself and if x is negative it is the positive value of the number

Ex. |5| = 5 and |-5| = 5

Take the absolute values of each of the numbers first

|12.3| = 12.3

|-20| = 20

|2 3/10 | = 2 3/10 = 23/10 = 2.3

|-4| = 4

|8| = 8

|-6| = 6

Now arrange these numbers from greatest to least. The order is

20,  12.3,  8,  6,  4,  2.3

So in terms of the original numbers this corresponds to
|-20| ,  |12.3| ,   |8|,   |-6| , |-4| , |2 3/10|

Michael has $96 in savings and makes $12.00 an hour at his job. Greg has $128 in savings and makes $10.00 an hour his job. They both save all their earned money. How many hours they both have to work to have the same amount of money saved?

Answers

The computation shows that the hours that they both have to work to have the same amount of money saved is 16 hours.

How to calculate the function?

Based on the information given, let the number of hours be represented by h

Therefore, the first function for Michael will be:

96 + 12h

The second function for Greg will be:

= 128 + 10h

Therefore, we'll equate both equations. This will be:

96 + 12h = 128 + 10h

12h - 10h = 128 - 96.

2h = 32.

h = 32/2

h = 16 hours.

Learn more about computations on:

brainly.com/question/4658834

#SPJ1

Find the sum of 0.55 and 0.41 i need help

Answers

The answer is 0.96 because you need to add them together

prove that the set of all xy=0 in R^n is not an open set

Answers

the set of all x y = 0 in R is not an open set.

x y = 0 in R is possible if

either x= 0y =0x = y = 0

So, the contains (0,0) , (0, any real number) ,...…..,

(any real number, 0) ,...…..

So, the set is not an open set.

Hence proved.

Therefore, the set of all x y = 0 in R is not an open set.

"Learn more about open set here - https://brainly.com/question/18567569 "

#SPJ9

I don’t know how to do this -2(-5+n)=6 ?

Answers

Answer:

n = 2

Step-by-step explanation:

So all you have to do is solve:

-2(-5 + n) = 6

= 10 + -2n = 6

= -2n = -4

= n = 2

This means that n = 2.

But what if I'm wrong? So lets see if it works.

-2(-5 + 2) = 6

10 - 4 = 6

6 = 6

So n = 2 is right.

Hope this helped! :D

Answer:

n = 2

Step-by-step explanation:

I don’t know how to do this -2(-5+n)=6 ?

-2*(-5+n)=6

10 -2n = 6

10 - 6 = 2n

4 = 2n

2 = n

-----------------

check

-2 ( -5 * 2) = 6

10 - 4 = 6

6 = 6

7.8 x 10 3
--------------
1.2 x 10 4

Answers

Step-by-step explanation:

7.8 ×1000=7800.

1.2×10000=12000.

7800÷12000=0.65.

8. Gavin goes to the market and buys one rectangle shaped board. The
length of the board is 16 cm and width of board is 10 cm. If he wants to add
a 2 cm wooden border around the board, what will be the area of the
rectangle board?

Answers

160 cm² is the area of the rectangle.

What do we mean by rectangles?A rectangle is a closed two-dimensional shape with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. Because a rectangle is a 2-D shape, it has two dimensions: length and width. The word rectangle is derived from the Latin word rectus, which means "right" or "straight." A rectangle has straight sides due to its right angles.Rectitude, which means moral uprightness, is another word with the same root.

The formula for the area of a rectangle:

l × b

Put values in the formula:

= 16 × 10= 160 cm²

Therefore, the area of a rectangle is 160 cm².

Know more about the area of rectangles here:

https://brainly.com/question/25292087

#SPJ9

Function yes or no whag is the domain and range?

Answers

Step-by-step explanation:

to be a function every value of x must have exactly one value of y.

in other words, if you create a vertical line and move it across the whole chart (e.g. from left to right), this line must not even once intersect the function curve more or less than once.

so, this is clearly a given here. yes, it is a function.

the domain is the interval or set of all valid x (input) values. and that starts on the right with x = 5 (included in the function indicated by the filled dot). and it goes endlessly to the left. that means -infinity (but not included as "infinity" is only a symbol but not a number).

-infinity < x <= 5

the range is the interval or set of all valid y (function result) values.

and that starts on the top with y = 2 (included). and it goes endlessly down. that means again -infinity (not included).

-infinity < y <= 2

50 points please show your work and answer all of them

Answers

Answer/Step-by-step explanation:

Convert:

8m to _800_cm

K     H     D     B     D     C     M

                     8 -> 80 -> 800      

---------------------------------------------------------------------------------------------------

Interpret and simplify:

1 added to the difference of 12 and 9

1 + (12 - 9)

1 + (3) = 4

---------------------------------------------------------------------------------------------------

Write a positive or negative integer that represents the following:

A football team loses 14 yards on a play.

loses indicated a negative

-14

------------------------------------------------------------------------------------------------------

Evaluate:

  4          3

------- + -------

 20        12

  4 (3)     3 (5)

------- + -------

 20 (3)   12 (5)

 12          15         27

------- + -------  =  -------

 60        60         60

 27 ÷ 3           9

-------     =     --------

 60 ÷ 3          20

----------------------------------------------------------------------------------------------------------

Write the Prime Factorization of 24.

             24

            /    \

          2  ×  12

                  /  \

                2 × 6

                     /  \

                   2 × 3

Prime factorization = 2 × 2 × 2 × 3 or 2³ × 3

----------------------------------------------------------------------------------------------------------

Tell whether the ordered pair is a solution of the equation:

y = x + 7; (1, 6)

               (x, y)

6 = 1 + 7

6 = 8

Not a solution

----------------------------------------------------------------------------------------------------------

Simplify and Graph the following:

x = -2 - 3

x = -5

      ↑

<-----|--------------------------------->

      -5

      ↓

Don't worry about the other numbers. Put a dot on -5 and draw a line vertically (up and down).

----------------------------------------------------------------------------------------------------------

If the weight of a package is multiplied by (5/7). The result is 40.5 pounds. find the weight of the package.

x(5/7) = 40.5

---------  --------

÷(5/7)   ÷(5/7)

x = 56.7

----------------------------------------------------------------------------------------------------------

A = (1/2)bh

A= (1/2)(8)(5)

A = (1/2)(40)

A = (20)

A = 20in²

----------------------------------------------------------------------------------------------------------

I hope this helps!

Which is the better deal? 16 oz of jelly for $3.30 or 48 oz of jelly for $8.64

Answers

Answer: The 48 0z of jelly for 8.64

Step-by-step explanation: because 16 oz of jelly is 3.30 and if you double it, it is $9.9

Answer:

48 Oz of jelly for $8.64

Step-by-step explanation:

16oz of jelly is $3.30 x 3 =$9.90

Help!! Find the domain of the graphed function.

Answers

it would be b, x is greater than or equal to 0

if you were to look at the x coordinates from any point in the function, it’s always more than 0 (the first point is 0). every x point is greater than 0 so it can’t be all real numbers since that would include negative x coordinates

can someone answer this please

Answers

can someone answer this please. done

Find the sum of (4.9 × 10^−9) and (7.4 × 10^−10). Write the final answer in scientific notation.
5.64 × 10^−9

5.64 × 10^−10

1.23 × 10^−18

12.3 × 10^−19

Answers

Taking into account the scientific notation, the result of the sum is 5.64×10⁻⁹.

Scientific notation

Scientific notation is a quick way to represent a number using powers of base ten.

The numbers are written as a product:

a×10ⁿ

where:

a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.n is an integer, which is called an exponent or an order of magnitude. Represents the number of times the comma is shifted. It is always an integer, positive if it is shifted to the left, negative if it is shifted to the right.

Sum in scientific notation

To add two numbers in scientific notation, when the numbers to be added do not have the same base 10 exponent, the base 10 power with the highest exponent must be found. In this case, the highest exponent is -9.

Then all the values ​​are expressed as a function of the base 10 exponent with the highest exponent. In this case: 7.4×10⁻¹⁰= 0.74×10⁻⁹

Taking the quantities to the same exponent, all you have to do is add what was previously called the number "a". In this case:

4.9×10⁻⁹ + 0.74×10⁻⁹= (4.9 + 0.74)×10⁻⁹= 5.64×10⁻⁹

Finally, the result of the sum is 5.64×10⁻⁹.

Learn more sum in scientific notation:

brainly.com/question/11403716

brainly.com/question/853571

#SPJ1

What are the vertex and x-intercepts of the graph of y = x2 – 4x – 21? Select one answer for the vertex and one for the x-intercepts. A. x-intercepts: (–3, 0), (7, 0) B. x-intercepts: (3, 0), (7, 0) C. x-intercepts: (3, 0), (–7, 0) D. Vertex: (2, 13) E. Vertex: (2, –25) F. Vertex: (–2, –9)

Answers

Answer:

To find x-intercept ,let y=0

0=x²-4x-21

(x+3)(x-7)=0

x=-3 or x=7

(-3;0) or (7;0)

To find vertex

x=

[tex] \frac{ - b}{2a} = x[/tex]

x=4/2=2

y=(2)²-4(2)-21=-25

(2;-25)

choose A and E

Estimate using compatible numbers then find quotient 62÷1178

Answers

Answer:

the answer would be 0.05

g(x)=3x+1
f(x) =x^2 + 3x^2
Find g(2)•f(2)

Answers

Answer:
112

Step-by-step explanation:

Just plug in 2 into the equations and then multiply them together at the end.

g(2) = 3(2) + 1
       = 6 + 1
       = 7

f(2) = (2)² + 3(2)²
      = 4 + 3(4)
      = 4 + 12
      = 16

g(2) × f(2)
    7 × 16 = 112

Can someone please find x ?

[tex]\frac{4}{3} x- \frac{1}{3} = x + 7[/tex]

Answers

the value of x in the question is 22

How to determine the value of x?

The equation is given as

4/3x - 1/3 = x + 7

Multiply through by 3

4x - 1 = 3x + 21

Collect the like terms

4x - 3x = 1 + 21

Evaluate

x = 22

Hence. the value of x in the question is 22

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

can u guys please help me with is problem!! (ᗒᗩᗕ|||)​

Answers

Answer: 4 miles per hour

Explanation: Put in the calculator 1/7 divided by 1/28 and then you get 4. Also can I get the brainliest pls?

B is between A and C. If
AB=x+4 , BC=2x−2 , and AC=4x−1 , what is AB?
AB= (geometry someone help)

Answers

If B is between A and C and AB= x+4,BC= 2x-2 and AC= 4x-1, then the length of the AB is 3 units

The point B is between A and C

AB = x+4

BC = 2x-2

AC = 4x-1

We know,

AC = AB + BC

Substitute the value in the equation and find the value of x

4x-1  = x+4  + 2x-2

4x-1 = 3x-2

4x-3x = -2+1

x = -1

Then,

AB= x+4

Substitute the value of x in the equation

AB = -1+4

AB = 3 units

Hence, If B is between A and C and AB= x+4,BC= 2x-2 and AC= 4x-1, then the length of the AB is 3  units

Learn more about length here

brainly.com/question/17281779

#SPJ1

I need help for the Wednesday one

Answers

Answer:

Seth is correct.

Step-by-step explanation:

Complementary means that they add to 90 degrees.  Supplemental means that they add to 180.  147 + 33 equals 180 so they are supplemental.

13.95 + 0.49x = 50 - 13.95 - x
Whats the value of x please i have a test today

Answers

Answer:

14.832

Step-by-step explanation:

I hope this helps good luck

At Gabby's family reunion, Gabby hands out watermelon for the annual seed-spitting contest
She gives a watermelon slice to each kid at the reunion. She also gives a slice to 25 adults.
Gabby hands out 55 watermelon slices in all.
Which equation can you use to find how many kids k are at the reunion?
k - 25 = 55
k
25
= 55
k + 25 = 55
25k = 55
Solve this equation for k to find how many kids are at the reunion.

Answers

The  equation which can be used  to find how many kids k are at the reunion is :k + 25 = 55

There are 30 kids at the reunion

What is algebraic expression?

Algebraic expressions are based on expressing numbers using letters  without indicating their actual values, such that we can determine the unknown variables by solving the expression or equation.

The total number of watermelons in this case is 55, if 25 slices are handed to the adults in the reunion gathering, the remaining one is the difference between 55 and 25 already served, which is known as k in this case.

total number of watermelons=55

number of adults=25

number of kids given watermelon=k

i.e k+25=55

k=55-25

k=30

Find out more algebraic expressions on:brainly.com/question/14662537?

#SPJ1

Mark won 83 lollipops playing hoops at
the county fair. At school he gave three to
every student in his math class. He only
has 8 remaining. How many students are
in his class?

Answers

Answer: 25 students

Step-by-step explanation:

Answer:

25 students

Step-by-step explanation:

83 lollipops - the 8 remaining lollipops = 75 lollipops

75 lollipops ÷ 3 ( the amount he gave to each student) = 25

3 lollipops per person

3 * 25 people = 75 + 8 (remaining)

Complete the statement.
x(y + 5) = x(__) + x(__)

Answers

Answer:

x(y + 5) = x(y) + x(5)

Step-by-step explanation:

Multiply the x to the variable and number in the parenthesis.

Can also be written xy + x5.

Ksjshshdieiwbehdjjejeebbejsjshs

3) A closed rectangular box with volume 12 cubic feet is such that the length of its base is twice
the width. Express the surface area of the box as a function of the width.
Point Breakdown
1) 8 points (4/4)
2) 6 points
3) 6 points

Answers

A closed rectangular box with volume 12 cubic feet is such that the length of its base is twice the width.The surface area of the box as a function of the width is (4b³ +36)/b.

volume 12 cubic feet

volume =(l)(b)(h)=12

l=2b

(2b)(b)(h)=12

h=6/b²

Surface area =  2 (lb + bh + lh)

 = 2((2b)(b) + b(6/b²) + 2b(6/b²))

=4b² + 12/b + 24/b

 = (4b³ +36)/b

A three-dimensional object's surface area is the sum of all of its faces. Real-world applications of the notion of surface areas include wrapping, painting, and finally constructing things to get the greatest potential design.

An object's surface area is the total area that all of its surfaces occupy. The formulae we will learn in this post make it simple to determine the various surface areas that various 3D forms in geometry have. There are two groups for the surface area:

The surface area that is laterally oriented or curved

Surface area overall

To learn more about surface area visit , https://brainly.com/question/2835293

#SPJ9

PLEASE HELP DUE SOON!
I'm so confused, help determine the 100th line segment from question below!

Answers

Answer:

20200

Step-by-step explanation:

As you're in a hurry, I can give it later? xx

Rieko has 10 pounds of nails. She divides the nails equally among 3 bags. How many pounds of nails does Rieko place in each bag?

Answers

A division is a process of splitting a specific amount into equal parts. The number of pounds Rieko place in each bag is 3.33 pounds.

What is division?

A division is a process of splitting a specific amount into equal parts.

We have,

Rieka has 10 pounds of nails and wants to divide it equally among 3 bags.

We need to divide the 10 pounds by 3.

The number of pounds in each bag:

= 10 pounds / 3

= 3.33 pounds

Thus the number of pounds in each bag is 3.33 pounds.

Learn more about division here:

https://brainly.com/question/787314

#SPJ1

What is the ones digit in the number 2^2076Hint: Start with smaller exponents to find a pattern.
Answer

Answers

Answer:

Step-by-step explanation: i think 9 the 9 is in one digits

determine a series of transformations that would map polygon abcd onto polygon a'b'c'd​

Answers

Answer: a reflection across the y-axis and scaling it by a factor of 1/2

Step-by-step explanation: First, you need to reflect the shape over the y-axis to move it into the neighboring quadrant. After that, you scale the polygon down by a factor of 1/2, because the lengths of the line segments of A'B'C'D' are half the length of the original polygon, ABCD.

Other Questions
suppose a frequency distribution has the following consecutive classes: $20 up to $30 $30 up to $40 $40 up to $50 what is the class midpoint for the first class? Find the mean, median, mode(s), and range of the data.1. Marianne's Daily Earnings at a Part-Time Job:$20, $22.50, $20, $27.50, $25 I NEED IT RIGHT NOW!!! Maritsa is making a necklace of x wooden beads at 0.60 each and 11 glass beads at $1.55 each. The total cost of the necklace is $21.85. Write an equation to esent this situation. What English word has three consecutive double letters?This word actually refers to someone who loves numbers. issued by a nonfinancial firm, these financial instruments are guaranteed by a bank. there is less risk involved because of bank backing. 000Cedric lives in an apartment and pays the following expenses each month: electric bill,$33.90; TV streaming service, $24.99; and rent, $538.95. Estimate his total expenses forthe month by first rounding each value to the nearest tens place.O $550O $590O $598O $600 The sum of three consecutive odd integers is -33. Find the value of the least of the three. the story concerning the discovery of starbucks frappuccino is an example of a(n) strategy, or an unplanned strategic initiative that originated at the bottom and moved to the top. I need help with this!!! what is a KWLQ chart ill give brainest as compared to other types of deeds, a general warranty deed provides the most comprehensive warranties about the quality of the title to the property. piercewill08 is officially on my list of "reliable answers" Are we alone to ask and take the utmost that our women can give, "service and sacrifice of every kind, "and still say we do not see what title that gives them to stand by our sides in the guidance of the affairs of their nation and ours? "president woodrow wilson, address to the senate, 1918 why did president wilson support the nineteenth amendment? check all that apply. women deserve the right to participate. society does not give women the same responsibilities as men. women share the burden of supporting the nation. women do not contribute to the nation. it is hypocritical to deny women the right to vote. Vanillin is a flavoring agent which occurs naturally in the vanilla bean, the seed of an orchid. identify the functional group circled. carboxylic acid aldehyde carbonyl alcohol ketone A 2.36 cm3 sample of an unknown metal weighs 18.5 g. what is the sample's density? On April 24th, Turkey celebrates National Sovereignty Day to commemorate the founding of its government. April 24th is also a special day for Armenians, called Armenian Genocide Remembrance Day. Some have lobbied to make this an official day in Turkey as well, but the Turkish government insists that this would distract from celebrating the founding of their country. For what other reason is the Turkish government MOST likely opposed to recognizing Armenian Genocide Remembrance Day?A. If they recognize the genocide, they might have to pay millions in reparations to descendants.B. There are not any Armenians who live in Turkey so it would not make sense to celebrate it in their nation.C. The current leader of Turkey was one of the men involved in the murder of millions of Armenian citizens.D. The Turkish government has true documentation to prove that there was no such thing as the Armenian genocide. Assume that you are the owner of a small bicycle sales and repair shop serving hundreds of customers in your area. Identify the kinds of customer information you would like your firm's Customer Relationship Management (CRM) system to capture. How mighthis information be used to provide better service or increase revenue? Identify where or how you might capture this data. when research participants are told enough information to help them decide whether they want to participate, it is called . 1. Cul o cules son los interceptos con el eje x , de la funcin2.Especifica una ecuacin cuadrtica para las siguiente raz:3.Las soluciones de la ecuacin4.Usa la discriminante para determinar la naturaleza de las races de las ecuaciones.5.Plantea una ecuacin cuadrtica para la parbola PLS HELPSHOW WORK------------------------------