use eitz = (x²)" n=on! to find 9(6) (0) (the sixth derivative evaluated at O).

Q: п(п+1) Уn(п + 1)x" оg 3" n=1 n=1

A: Given function is f(x)=11-x power series of above function is 11-x=∑n=0∞xn…

Q: Find the coefficient of x° in the power series of this function f(x) = (1–2x)2

A:

Q: FIND THE TAYWR FUR f (x) = 7 X4 SERIES ABOUT X=-3

A:

Q: The question is to find a power series for the function centered at c f(x) = 5/(5-x) , c = -3

A:

Q: find a power series representation for f(x) ln(14 -x)

A:

Q: For number 7, can you show why C= 3-ln4 when x=3. And can you show why the series diverges when x=5?

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Q: the common difference of the AP.

A: A

Q: Find the coefficients of the power series c0, c1, c2, c3, c4 for f(x)=ln(1-x^2)?

A:

Q: Find a power series for the function f (x) = x2/(1 + x3)

A: We have to find the power series for the function f (x) = x²/(1 + x³)

Q: y" + 3xy + 3y = 0 , y(0) = 1, y (0) = 0 . %3D %D

A:

Q: Obtain the 5th term of the power series of sin(x) for a value of x = 4.55.

A:

Q: Use the exponential series to find an approximation to e-1 correct to three significant figures.

A: we know that,ex=∑n=0∞x2n!⇒ex=1+x1!+x22!+x33!+x44!+x55!+x66!+x77!+x88!+···putting…

Q: Find the power series representation for the derivative of the function

A:

Q: Σ (-1)"(n + 1)n² (2n)! -2n+1 — — п n=0

A: Find a power series representation for x2cos(2x).

Q: f(x) = = 1 1 + x for-1 < x < 1. The base point is 0.

A:

Q: 2) Determine the solution to the equation y' = y + x² using the following methods b.) power series

A: We have to solve given problem:

Q: Determine a power series representation for g(x)=x° cos(x). CoS

A: Solve the following

Q: 13.) Find a power series for the function f(x): = 5 2-6x3*

A: