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3 years ago

Does this graph show a function?

Mathematics

1 answer:

Mashutka [201]3 years ago

8 0

Answer: a

Step-by-step explanation:

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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

aliya0001 [1]

Answer:

$f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}$

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

$f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...$

We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

$f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\$

Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

3 0

3 years ago

Every week, Bob plays the guitar for three hours, and his grade on each psych test is 75 percent. Last week, after playing fo

dsp73

Answer:

20% psyche test scores

Step-by-step explanation:

Given that every week, Bob plays the guitar for three hours, and his grade on each psych test is 75 percent.

Last week, after playing for three hours, Bob considered playing for an additional hour.

He decided to play for another hour and cut his study time by one hour, but last week his psych grade was 55 percent.

Bob's opportunity cost of the fourth hour of playing the guitar

=His cut in scores in psyche test

=20%

4 0

3 years ago

Jackson is three times as heavy as Andrew. If the sum of their weight is 360 pounds, find Andrews weight

Delicious77 [7]

Answer: Andrew = 90 pounds

Explanation:
Assume Andrew weight is X
Since Jackson weight is 3 times Andrew
Then it’s 3x

3x + x = 360
4x = 360
x = 90

5 0

3 years ago

Read 2 more answers

If (x + 2) is a factor of x3 − 6x2 + kx + 10, k =

ch4aika [34]

Answer:

The value of k is -11

Step-by-step explanation:

If (x+2) is a factor of x3 − 6x2 + kx + 10:

Then,

f(x)=x3 − 6x2 + kx + 10

f(-2)=0

f(-2)=(-2)³-6(-2)²+k(-2)+10=0

f(-2)= -8-6(4)-2k+10=0

f(-2)= -8-24-2k+10=0

Solve the like terms:

f(-2)=-2k-22=0

f(-2)=-2k=0+22

-2k=22

k=22/-2

k=-11

Hence the value of k is -11....

5 0

3 years ago

-4(7a+5) = -160 Show All Work!

Fynjy0 [20]

Answer:

a=-20

Step-by-step explanation:

-4(7a+5)=-160

7a+(-20)=-160 Multiply -4 and 5

7a=-140 Subtract -20 from -160

a=-20 Divide 7 by -140

7 0

3 years ago