Find the first 3 terms of the Taylor series for f(x) = ln(x) centered at 4.

Q: find 5 th terms of the function{ sin(2x) }using Taylor series at a= pi/6

A: We will find out the required term.

Q: The first derivative of the power series D (-1)" (2x)" is n! f(x) = n=0

A: Given : fx=∑n=0∞-1nn!2xn As    e-ax=∑n=0∞-1nn!axn∴e-2x=∑n=0∞-1nn!2xn Therefore, fx=e-2x   .....1

Q: where f(x) = 5 x^ by identifying it as the value of a derivative or integral of geometric series. as…

A: Given that: fx=∑n=0∞xn Which is the sum of geometric series. Derivative of the function is:…

Q: find the Taylor series about x = 0

A: The Taylor series of a function f(x)  at  a point x=a is defined by the formula…

Q: Q1; Find Taylor series of the function f(x) = Vx at a = 36. ( piul) %3D

A:

Q: Create a Taylor Series for y =sin(x2) centered at x = 0 and a series for y=ln (√x) centered at c =…

A: Given y=sinx2 at x=0 We know that the Taylor series for y=sin x at x=0 is y=sin…

Q: b) Obtain a Taylors series of degree three for the function f(x) = log (1+2x) near x = 1 hence…

A:

Q: 3. Expand the function f(x)=x (4-x²) in the interval -2 ≤x≤2 and period f(x+4)= f(x) to the Fouriér…

A: Solution :-

Q: cosh(x) dx is The power series representation of

A:

Q: Find a power series expansion for f(x)=1/x.

A: Here we have to find out power series expansion of f(X).

Q: 9 Write the Taylor Series for f(x) = sin(x) at x = 12/12/2 as & Cn (x-7) n Find the first 5…

A: Taylor serues

Q: f (x) = arctan(r²)

A: We know that power series of arctan(x)

Q: Solve the ODE using power series. y'' + x^2y=0,  y(0)=0

A: Consider the given differential equation as y''+x2y=0 with initial value y0=0. Let the power series…

Q: Let f(x)=x² cos(√x).

A: Given function f(x) as follows :-   f(x)=x2cos⁡(x)   To find power series of derivative of f(x)…

Q: DO 11/2 x cos x² clx

A:

Q: find 5 th terms of the function{ sin(2x) }using Taylor series at a= pi/6

A: We will find out the corresponding term.

Q: Write the taylor series cetered at c = 1 for f(x) = 3x

A: The Taylor series of function f(x) centered at x=a is given by: f(x)≈∑n=0∞f(n)(a)n!(x-a)n