Taylor Polynomial Question?

Question

I know that increasing the degree of the polynomial makes it a better approximation, but what happens when i change the about x=0 to lets say... x=5? What happens?

Answer 1

A Taylor Polynomial is used to approximate points near the starting point you use. Changing it to x=5 would give you a better approximation for numbers that are close to 5 but a worse approximation for numbers that were near 0.