Linear approximation given accuracy points

[Hemolymph]

Homework Statement

Use a graphing calculator or computer to verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Round the answers to two decimal places.)
tan(x) ≈ x

Homework Equations

derivative of tan(x) = sec^2(x)

The Attempt at a Solution

f(0)= tan(0)=0
fprime(0)= sec^2(0)= 1
L(x)=f(a)+fprime(a)(x-a)
L(x)=0+1(x-0)
L(x)=x

not sure how to continue from here

 

[SammyS]

Homework Statement

Use a graphing calculator or computer to verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Round the answers to two decimal places.)
tan(x) ≈ x

Homework Equations

derivative of tan(x) = sec^2(x)

The Attempt at a Solution

f(0)= tan(0)=0
fprime(0)= sec^2(0)= 1
L(x)=f(a)+fprime(a)(x-a)
L(x)=0+1(x-0)
L(x)=x

not sure how to continue from here

I don't think you need to derive the result.

Graph y=tan(x) and y=x for -1 ≤ x ≤ 1 or some similar interval near zero.

Make a table of x and tan(x) for some values starting at x=0, and continuing until you have a difference of 0.1.