Find Tolerance Limit for f(x)=x^2.5 Near 0

[mnzavislan]

Homework Statement

Consider f(x)=x^2.5. Note that limf(x) as x->0+ =0. The input must be less than ___ from 0 to guarantee the output is within 0.1 of the limit.

Homework Equations

N/A

The Attempt at a Solution

 

[SammyS]

What have you tried?

Where are you stuck ?

 

[mnzavislan]

If I'm correct, the output can be 0.1 and -0.1. So I have computed:
f(0.1)= 0.00316 and f(-0.1)= -0.00316
These are the inputs that guarantee the output to be within 0.1 of the limit, 0. However, I think there is an error in my thinking somewhere.

 

[SammyS]

You used 0.1 as an input.

Solve f(x-0) = 0 + 0.1 for x.

 

[mnzavislan]

Ohhh okay! Got it. Thank you so much.