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4 years ago

I need help on this!

Mathematics

1 answer:

SSSSS [86.1K]4 years ago

8 0

Answer:

Read below

Step-by-step explanation:

2 and 4 would add up to be 6 at the higher part, right? so what would 4 and 6 add up to be? 10! so then 6 and 7 would be 13 and 7 and 3 would be 10. Then just keep going up. The rule is adding.

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Can someone plz help me with this one problem plz!!!

Lady bird [3.3K]

2,14 4,16 6,18 8,20 f=s+12

4 0

3 years ago

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

Simplify 5y^-2<br><br> please help fast!!!

Semmy [17]

Answer:

25y2 i think

Step-by-step explanation:

i hope it helps

4 0

2 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=3%20%5Cdiv%20441%20%3D%20" id="TexFormula1" title="3 \div 441 = " alt="3 \div 441 = " align="a

laila [671]

This is the decimal answer 0.00680272108

3 0

3 years ago

Please help me. I can't figure out how to get an equation

Eddi Din [679]

A printer shop purchases a new printer fro $25,000
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8 0

4 years ago