B. Find the first 4th terms for expansion of f(x)= In(1+3x) by using Mclaurin's Series.

Q: Find the Maclaurin series for the given function f(x) = e-6x

A: The maclaurin series is: f(x)=e-6x     ,    f(0)=1f'(x)=-6e-6x     ,    f'(0)=-6(1)=-6f''(x)=36e-6x…

Q: What is the coefficient of x4 in the MacLaurin series for f(x) = e^(-x/2)?

A: Here we will find out the required value.

Q: f(x) x² + 3

A: Find the power series expansion of  f(x)

Q: Q2 Find the Maclaurin Series expansion for the function, 1 f(x) = (1– 4x)³ by writing the first four…

A: We have to find Maclaurin's series expansion for the given function by writing first four non zero…

Q: Find the Maclaurin series for f(x) = e^(5x) , at a=0

A: The solution is given as

Q: Find the first 5 nonzero terms of the Maclaurin series for f(x) = e^(2x)

A:

Q: Write the first four terms of the Taylor series for f(x) = In(x) centered at C= 1.

A:

Q: Use sigma notation to write the Taylor series about x = xo for the function. In x; xo 1 EO (-1)*+1…

A:

Q: Use sigma notation to write the Taylor series about x = xo for the function. 6 In r; xo = 1

A:

Q: Find the coefficient of x in the power series expansion of f(x) = 2x1

A: Given the function

Q: Write the first four terms of the Maclaurin series for f(x) = ln(x+1)

A: see 2nd step

Q: Find the power series representation for the given function: f(x) = In(1 – 2x)

A: The power series of given function f(x) is given by fx=∑n=0∞anx-x0n Where ai's are constants…

Q: Find the first four nonzero terms in the Maclaurin series for the functions ln (1 + x)/1 - x

A: Given: f(x)=ln1+x1-x We have to find the first four nonzero terms in the Maclaurin series for…

Q: Find the first five terms of the Maclaurin series for f(x) = x sin x +1

A:

Q: Find the Maclaurin series for the given function. f (x) = 3"

A: We need to find , Maclaurin series for , fx = 3x. We know that , Maclaurin series is given by ,  fx…

Q: Find the first four nonzero terms of the Mclaurin's series for function f (x) = sin 2x.

A:

Q: Q2 Find the Maclaurin Series expansion for the function, 1 f(x) = (1 – 4x)2 by writing the first…

A: We need to find the Maclaurin series expansion of 1/(1-4x)2.

Q: 1 of the function f (x) = and put the series in

A:

Q: 4. Find a power series representation for f(x) = 9+ x2

A:

Q: Find the Maclaurin series for the functions e-x

A: The given function is, fx=e-x The Maclaurin Series is given by,…

Q: Find a geometric power series centered at e = 0 for the function: 2.x h(x)=- x' -1

A:

Q: Find the Maclaurin series expansion of degree 4 for the function f (x) = xe**-2 %3|

A: fx=xex2-2Maclaurin series…

Q: Q2 Find the Maclaurin Series expansion for the function, 1 f(x) = (1+ 2x)3 by writing the first four…

A: Given that:

Q: Q4: Find the Mackurin series for function f(x)=Jx+1

A: Given function: fx=x+1 To write: The Maclaurin series for the function fx. Formula used: The formula…

Q: 8. Use sigma notation to write the Taylor series about xo=1 for f(x) = e*-1.

A:

Q: Q2 Find the Maclaurin Series expansion for the function, 1 f(x) = (1- 4x)2 by writing the first four…

A:

Q: Find the Maclaurin series for f(x) = ln(1 + 2x).

A:

Q: 12. Find the Maclarin Series expansion for f(x)= sin 7x.

A: Maclaurin Series for f(x) : f(x)=∑n=0∞ fn(0)n!xn =f(0)=f'(0)x+f''(0)2!x2 +f'''(0)3!x3+...

Q: (a) Find the Taylor's series for the function f(x)= In(3+4x) at x= 2.

A: The Tayler's formula can be used to calculate the expansion of the function. The formula for the…

Q: 12) Find the Maclaurin Series for the function f(x) = (x + 5)-1.

A:

Q: What is the coefficient of x^4 in the Maclaurin series for f(x) = e^(-x/2)?

A:

Q: Find the Maclaurin series for the function x2>(1 + x).

A:

Q: Use sigma notation to write the Taylor series about x = xo for the function. 10 In x; xo = 1 k =

A:

Q: 5) (a) Derive the Maclaurin series for the function f(x) = + 1 in its simplest form, up to and…

A:

Q: f (x) = ln (3x + 1)

A: To find- Maclaurin series of f(x).

Q: Find the first four nonzero terms in the Maclaurin series for the function. f(x) = In (1 + x³)

A:

Q: Find a power series representation for f(x) = V1 + x.

A: Consider the function

Q: Find the first three terms of Maclaurin series for F(x) = In (x+3)(x+3)²

A: A Maclaurin series is a special case of a Taylor series, obtained by putting x = 0 i.e.,

Q: Find the first five terms of the Maclaurin series for f(x) = x sin x + 1

A:

Q: Find the half - range cosine series expansion of f(x)=x-x' in 0<x<1.

A: The required series is of the form x-x2=a02+∑n=100ancos nπx where an=2∫01x-x2cos nπx dx (∵l=1) =…

Q: Use sigma notation to write the Taylor series about = xo for the function. In x; xo k =

A:

Q: Find the Maclaurin series for the function. f(x) = In(1 + x 00 Σ F(x)

A: We consider the series  1/(1-x) = Summationn = [0 to infinity] (xn) this has radius of convergence R…

Q: Q2 Find the Maclaurin Series expansion for the function, 1 f(x) = %3D (1 + 2x)3

A: We can use series expansion of (1+x)-n.

Q: Use the Maclaurin series for the exponential function Σ xn e* = п! n = 0 To evaluate the limit е 3x…

A:

Q: Use sigma notation to write the Taylor series about x = 4 for the function. 1 x + 3 1 -1* 7*+1 (x –…

A:

Q: Find the first three nonzero terms in the Maclaurin Series of f(x)=e^x sin x

A:

Q: (b) Use part (a) to find a power series for 1 f(x) %3D (7 + x)3 ° f(x) = %3D n = 0

A:

Q: 1 Find the Maclaurin series for the function f(x) : 2-x

A:

Q: Find the power series representation for the given function: f (x) = In(1 – 2x)

A: We have to find the power series representation of the given function: fx=ln1-2x We know that,…

Q: 2 Find the Maclaurin series for the function g(x) = (x)

A: Given:          gx=cosx2          gx=cos2x   A Maclaurin series is given by gx=∑k=0∞f(k)ak!xk…