# What are the first 3 nonzero terms in the Taylor series expansion about x = 0 for the function #f(x)=cos(4x)#?

Because

so

By signing up, you agree to our Terms of Service and Privacy Policy

The first 3 nonzero terms in the Taylor series expansion about ( x = 0 ) for the function ( f(x) = \cos(4x) ) are:

[ f(x) = \cos(4x) ]
[ = \cos(0) + \left( \frac{d}{dx} \cos(4x) \right)*{x=0}x + \frac{1}{2!}\left( \frac{d^2}{dx^2} \cos(4x) \right)*{x=0}x^2 + \cdots ]

Where ( \cos(0) = 1 ), the first derivative of ( \cos(4x) ) at ( x = 0 ) is ( -4 \sin(0) = 0 ), and the second derivative is ( -16 \cos(0) = -16 ). Therefore, the expansion becomes:

[ f(x) = 1 + 0 \cdot x - \frac{16}{2}x^2 + \cdots ]

So, the first 3 nonzero terms are ( 1 ), ( 0 ), and ( -8x^2 ).

By signing up, you agree to our Terms of Service and Privacy Policy

- What is the interval of convergence of #sum_1^oo [(2n)!x^n] / ((n^2)! )#?
- What is the radius of convergence of the MacLaurin series expansion for #f(x)= sinh x#?
- How do you find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a f(x) = cos(x), a= pi/4?
- How do you find the taylor series for #f(x) = cos x # centered at a=pi?
- What is the Maclaurin series for #(1-x)ln(1-x)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7