Linear Approximation of Tanx at a=0: Determining Accuracy Within 0.1

[fk378]

Homework Statement

Verify the linear approximation tanx = x at a=0.
Then determine the values of x for which the linear approximation is accurate to within 0.1.

Homework Equations

L(x)=f(a) + f'(a) (x-a)

The Attempt at a Solution

Besides writing down that tanx - 0.1 < x < tanx + 0.1
I have no idea how to approach this!

 

[Dick]

If you want an 'exact' answer (to some number of signficant digits) to that inequality you would have to solve it numerically. I suspect they want you to estimate a remainder term to the Taylor series. What forms of that do you know?

 

[fk378]

I don't know what the Taylor series is. I don't think they're looking for a numerical answer though. I think they're looking for some sort of proof? I just started learning linear approximations.

 

[Dick]

If you don't know what a Taylor series is, forget that suggestion. Just goof around with your calculator to figure out how big x can be and still keep |x-tan(x)|<0.1. There's not really a nice way to do it.