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

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: 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: 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