# 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?

##### 1 Answer

#### Explanation:

Remembering that any function

We can compute the required derivatives (in this case three) and find a general formula for our infinite sum.

Calculations:

Now that we have our derivatives at point

To check our answer, we can always graph both equations:

Graph of

graph{cos x [-7.9, 7.895, -3.95, 3.95]}

Graph of

graph{sqrt(2)/(2) - (sqrt(2)/(2)(x-pi/4))/(1!) - (sqrt(2)/(2)(x-pi/4)^(2))/(2!)+ (sqrt(2)/(2)(x-pi/4)^(3))/(3!) [-7.9, 7.895, -3.95, 3.95]}

Overlapping both graphs gives you the following:

If we increase the number of polynomial terms in our series we automatically make it a better approximation to our function.