# Homework Help: Linear approximations

1. Oct 2, 2007

### fk378

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
L(x)=f(a) + f'(a) (x-a)

3. The attempt at a solution
Besides writing down that tanx - 0.1 < x < tanx + 0.1
I have no idea how to approach this!

2. Oct 2, 2007

### 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?

3. Oct 2, 2007

### 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.

4. Oct 2, 2007

### 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.