# How do you find the taylor series for #f(x) = cos x # centered at a=pi?

The general formula for the Taylor Series is as follows:

Thus, we have to take the derivative multiple times. You should also consider the following:

Now, writing it out, we get:

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

To find the Taylor series for ( f(x) = \cos x ) centered at ( a = \pi ), we can use the formula for the Taylor series expansion:

[ f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} (x - a)^n ]

First, we find the derivatives of ( f(x) = \cos x ) up to the desired order at ( a = \pi ), which is the center of the Taylor series. Then, we substitute these derivatives into the Taylor series formula.

Here are the derivatives of ( \cos x ):

[ f(x) = \cos x ] [ f'(x) = -\sin x ] [ f''(x) = -\cos x ] [ f'''(x) = \sin x ] [ f^{(4)}(x) = \cos x ]

Now, evaluate these derivatives at ( x = \pi ):

[ f(\pi) = \cos \pi = -1 ] [ f'(\pi) = -\sin \pi = 0 ] [ f''(\pi) = -\cos \pi = -1 ] [ f'''(\pi) = \sin \pi = 0 ] [ f^{(4)}(\pi) = \cos \pi = -1 ]

Substitute these values into the Taylor series formula:

[ \cos x = \sum_{n=0}^{\infty} \frac{(-1)^n}{n!} (x - \pi)^n ]

This is the Taylor series for ( \cos x ) centered at ( a = \pi ).

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

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the taylor series of #1 1x^2#?
- How do you do the taylor series expansion of #arctan(x)# and #xsinx#?
- How do you find the maclaurin series expansion of #f(x)=(1-x)^-2#?
- What is the interval of convergence of #sum_{k=0}^oo 2^(k) / ((2k)!* x^(k)) #?
- Find the sum of the series: #sum_{n=5}^ ∞ 6 / (n^2 - 3n)# ?

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