Problem:

Find the second Taylor polynomial for the function about

Use to approximate f(0.5). Find an upper bound for error using the error formula and compare it to the actual error.

Now

In mine case:

And substitute for and I need to find upper bound on for 0 < E(x) < 0.5

The upper bound is for E(x)=0.5 that is .

But in the solution manual it is 0.0532. I rechecked 10 times and I start to believe that it's their error.

Thanks in advance.