Answers
f ' (0) exists if the limit,
[tex]\displaystyle \lim_{h\to0}\frac{f(0+h)-f(0)}h[/tex]
exists, and f ' (0) has the value of this limit.
In order for this limit to exist, both limits from either side of h = 0 must exist.
Suppose h < 0. Then 0 + h is also negative, so by definition of f(x) we have
f (0 + h) = ((0 + h) + 1)² = h ² + 2h + 1
Then in the limit, if h is approaching 0, it must be from below or from the left:
[tex]\displaystyle \lim_{h\to0^-}\frac{f(0+h)-f(0)}{h} = \lim_{h\to0^-}\frac{(h^2+2h+1)-1}{h} = \lim_{h\to0^-}(h+2) = 2[/tex]
Now suppose h > 0, so that 0 + h is positive and h approaches 0 from above or from the right. Then
f (0 + h) = 2 (0 + h) + 1 = 2h + 1
and
[tex]\displaystyle \lim_{h\to0^+}\frac{f(0+h)-f(0)}h = \lim_{h\to0^+}\frac{(2h+1)-1}{h} = \lim_{h\to0^+}2 = 2[/tex]
Both one-sided limits match, so f ' (0) = 2.
Related Questions
A piece of wire 3/7 m long as we cut into six pieces of the same length what is the length of each piece
Answers
Answer:
Each piece is 1/7 m long
Step-by-step explanation:
Wire length = 3/7 m
Pieces = 6
1 piece = 3/7 ÷ 6
= 3/7 ÷ 6/1
= 3/7 × 1/6
= 1/7 m
You owe $1,753.42 on a credit card with a limit of $3,000.00 at a rate of 15.5% APR. You pay $400.00 the first 2 months and then
$200.00 until the bill is paid off. You pay the bill on the due date each month.
1) Complete the table showing the decreasing debt.
2) How much is your last payment?
3) What is the total amount paid by the time you pay off the credit card?
4) What was your debt ratio at the beginning?
Be sure to include in your response:
All parts of the table are complete and calculations correct
The answers to the additional questions
Month
Principal
Interest
accrued
Payment (on
due date)
End-of-
month
balance
Answers
9514 1404 393
Answer:
see attached$33.97$1833.970.584Step-by-step explanation:
1. We cannot be sure of your table headings, so we used ones that seem to fit. The completed table is attached.
The amount of interest is computed first. It is the product of the previous balance and the monthly interest rate: 0.155/12. This amount is rounded to cents, as it would be in real life.
The remainder of the payment after interest is paid goes to reduction of the principal amount owed. That payment to principal is subtracted from the previous EOM Balance to give the new end-of-month balance.
The total of payments to date is found in the Accrued Pmt column.
__
2. For the last payment, we made note of the interest owed and the outstanding balance, and added those values to get the payment amount. The result is the final balance is zero. The last payment is $33.97.
__
3. The total of all payments is $1833.97.
__
4. The "debt ratio" is presumed to mean the ratio of the credit card balance to the credit card limit. That ratio is ...
1753.42/3000 ≈ 0.584 . . . . "debt ratio"
_____
Additional comment
Various definitions of "debt ratio" are used by different folks for different purposes. Sometimes, it means the ratio of debt to income. Sometimes it means the ratio of minimum payments due to income. Here, we're not given any income information, so we presume the ratio is supposed to mean the fraction of credit limit that is being utilized.
You might need:
Find one value of x that is a solution to the equation:
(x2 – 6)2 = -3x2 + 18
X=
Answers
Answer:
[tex]x = \sqrt{6} [/tex]
Step-by-step explanation:
2(x^2 - 6) = - 3x^2 + 18
2x^2 - 12 = - 3x^2 + 18
5x^2 - 12 = 18
5x^2 = 30
x^2 = 6
x = square root (6)
Suppose the sum of two integers is negative. Must both be negative
Answers
Answer: Not necessarily. There are many ways to write a basic equation with a negative answer. For example, -3-4 = -7.
Step-by-step explanation:
Nikita bought a flat for rupees 4987653. Round off the price of the flat to the nearest thousands.
Answers
Model and Solve the problem.
5x1/2 Please hurry!!
Answers
please make me brainiest if helped!
Answer:
2.5
Step-by-step explanation:
i just did 5 times 0.5 hope this helped.
and 2.5 is greater then 2.05
HELP! Which expression is equivalent to a^b/c
Answers
Answer:
[tex]{ \rm{ {a}^{ \frac{b}{c} } \: \dashrightarrow \: ( {a}^{b}) {}^{ \frac{1}{c} } }} \\ \\ { \boxed{ \rm{ \boxed{} \: \: \sqrt[c]{ {a}^{b} } }}} \\ [/tex]
Dan and Brian have played 51 tennis matches.
Dan has won 29 times.
Brian won the rest.
a) Estimate the probability that Dan wins.
b) Estimate the probability that Brian wins.
Answers
Answer:
A = 29/51 B = 22/51
Step-by-step explanation:
(E) = number of favorable outcomes/ total number of possible outcomes
- number of possible outcomes= 51
- number of favorable outcomes= 29
therefore, P(E) = 29/51
- number of possible outcomes= 51
- number of favourable outcomes = 51 - 29 = 22
therefore, P(E)= 22/51
What is the product of -4.6 and 3.2?
Steps to get there would be helpful too!
Answers
Answer:-14.72
Step-by-step explanation:
Answer:
The answer is negative 14.72
Step-by-step explanation:
this is because if you multiply negative 4.6 and 3.2
Determine the value of x.
X 1
X 1.5
A)x=1
B)x=2.5
C)x=2
D)x=2.9
Answers
Answer:
The correct option is C. (x=2)
Step-by-step explanation:
Given
Length of the hypotenuse of the right angled triangle (h) = 2.5 cm
Length of one of the side (a) = 1.5 cm
Let the length third side be 'b' cm
By Pythagoras theorem
h² = a² + b²
Adding Values on both sides
⇒ (2.5)² = (1.5)² + b²
⇒ 6.25 = 2.25 + b²
⇒ 6.25 - 2.25 = b²
⇒ 4 = b²
⇒ √4 = b
⇒ 2 = b
⇒ b = 2
Plot all points that are a distance of 7 units from 4. What are their values?
Answers
Distance is the number of units between points.
The distance that are 7 units from 4 are: 11 and -3
A distance of 7 units from 4 means:
[tex]x - 7 = 4[/tex] or [tex]x + 7 =4[/tex]
Where:
x is the required distance
Solve for x in both equations.
[tex]x - 7 = 4[/tex]
[tex]x = 7 + 4[/tex]
[tex]x = 11[/tex]
[tex]x + 7 =4[/tex]
[tex]x =4 - 7[/tex]
[tex]x =- 3[/tex]
So, the distance that are 7 units from 4 are: 11 and -3
See attachment for illustration
Read more about distance at:
https://brainly.com/question/7942332
When x = 2, 10+ 3(12= (3x)) = ?
A. 12
B. 16
C. 26
D.34
E. 104
Answers
Answer: E
Step-by-step explanation:
7 divided by $15.02. Round it by the nearest cent. QUICK!!
Answers
-1, -2, -4, -8….
What is the 8th term for this geometric sequence!
Answers
-4....................just took the quiz..........
Answer:
-128
Step-by-step explanation:
-1, -2, -4, -8, -16, -32, -64, -128
you are multiplying the previous number in the sequence by 2
hope this helped :)
Find the area of the triangle.
6
8
Answers
Answer:
24
Step-by-step explanation:
the area formula for a triangle is
base x high
----------------
2
so 6x8=48 and divided by 2 is 24
Answer:
24
Step-by-step explanation:
8×6 then Divide by 2........
Find the perimeter of the triangle whose vertices are (−4,4), (−4,1), and (−8,−4). Write the exact answer. Do not round.
Answers
Answer:
Step-by-step explanation:
The perimeter of the triangle is [tex]3 + \sqrt{41} + 5\sqrt{5}[/tex] units
How to determine the perimeter?The coordinates are given as:
(−4,4), (−4,1), and (−8,−4).
Calculate the distance between the vertices using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(-4 + 4)^2 + (4-1)^2} = 3[/tex]
[tex]BC = \sqrt{(-4 + 8)^2 + (1+4)^2} = \sqrt{41[/tex]
[tex]AC = \sqrt{(-4 + 8)^2 + (4+4)^2} = \sqrt{80[/tex]
The perimeter is the sum of the side lengths.
So, we have:
[tex]P = 3 + \sqrt{41} + \sqrt{80}[/tex]
Expand
[tex]P = 3 + \sqrt{41} + 4\sqrt{5}[/tex]
Hence, the perimeter of the triangle is [tex]3 + \sqrt{41} + 5\sqrt{5}[/tex] units
Read more about perimeter at:
https://brainly.com/question/24571594
#SPJ6
What is 11,885 as a percentage (round to 2 decimal places X.XX)?
Answers
Answer:
9.25
Step-by-step explanation:
A loan is payed off in 15 years with a total of 250,000. It had 4% interest
Answers
Answer:
5.2%po joke Lang Hahahahahahah
Answer:
$137,339.88
Step-by-step explanation:
Use the compound interest formula and substitute the values given:
$250,000=P(1+0.0412)12(15)
Simplify using order of operations:
$250,000=P(301/300)180
Solve for P:
P=$250,000(301/300)180≈$137,339.88
Look at the pictuse below i would copy and paste but I can't copy a picture
Answers
Answer:
15
Step-by-step explanation:
The constant of proportionality is 15 books per shelf.
If you look at the graph, you can see that for every 1 shelf, there are 15 books. For 1 shelf, there are 15 books, and for 2 shelves, there are 30. And the pattern continues.
Let me know if you have any questions, thanks!
You would like to start a club for psychology majors on campus, and you are interested to find out what proportion of psychology majors would join. The dues would be $35 and used to pay for speakers to come to campus. You ask five psychology majors from your senior psychology honors seminar whether they would be interested in joining this club and find that four of the five students questioned are interested. Is this sampling method biased, and if so, what is the likely direction of bias
Answers
From the sample used to find out what psychology majors would join the club and if it is biased, we can say that;
- Yes, the sampling method is biased.
- The likely direction of the bias is because you only asked 5 people which
is not a significant percentage of those offering psychology majors and as
such the 4 out of 5 gotten is likely going to be an over estimation of those
who are willing to pay to join this club.
We are told that;
You want to start a club.This club is for psychology majors.You want to find the proportion of those in the psychology majors that will join this club you want to organize.Now, out of all the students offering psychology majors, you only asked 5 of them if they will be interested. Since 4 out of the 5 are interested and you want to use that to form a basis of the proportion of those interested , it would lead to sampling bias since the population is not adequately represented.Therefore, this would lead to sampling bias and thus the sample is biased.
Read more at; https://brainly.com/question/12637861
Trigonometry prove that LHS=RHS
Answers
Answer:
bc cot 0
Step-by-step explanation:
what is the decimal of 3/8
Answers
Answer:
3/4 in decimal form= 0.375
have a nice day <3
[tex] \frac{3}{8} [/tex]
to find:the decimal form
solution:to convert to decimal just divide the numerator by the denominator.
[tex] \frac{3}{8} [/tex]
[tex] = 0.375[/tex]
[tex]1sf = 0.4[/tex]
20pens cost #300 and 50pens cost #750
(a)is the cost of pens directly proportional to the number of pens?
Answers
Answer:
669
Step-by-step explanation:
Jaliyah wants to play a prank on her older sister at her birthday party. She has two bags of blue glitter that she's planning on filling a birthday hat with. To figure out how much glitter she needs to use, Jaliyah must first find the volume of the party hat. Find the volume of the party hat in cubic inches.
Height = 8.4 inches
Length = 5.3 inches
Answers
Answer:
44.52
Step-by-step explanation:
Volume = b * h
base times height
The height is 8.4 inches so 8.4 *
Length is the same as base so 5.4
8.4 * 5.4
if sn = 1395 a = 3 and d = 3 find and =?
Answers
Answer:
Simplify:=-1
Step-by-step explanation:
Shaniqua is taking a test. After 20 minutes she has 35 questions left. After 40 minutes she has 15 questions left. If Shaniqua takes the same amount of time for each question how many questions are on the test
Answers
There were 55 questions in the test.
Answer:
55
Step-by-step explanation:
Evaluate -c when c = 12
Answers
Answer: [tex]-12[/tex]
Step-by-step explanation:
[tex]-c=-(12)=\boxed{-12}[/tex]
which expression is equivalent to -8m-8+3m-6?
-11m-2 -5m-2
-5m-14 or -16m-3
I need help!!!!
Answers
4x^2 times what equals -5x^2
Answers
Answer:
-1.25
Step-by-step explanation:
-5/4=
-1.25
check answer
4*-1.25= -5
given that x is an acute angle and cos x equals to 2 root 5/5 find without using mathematical tables or a calculator tan (90 - x)
Answers
Answer:
whats cos? i dont understand if its written in question please explain
Step-by-step explanation: