I am supposed to use Taylor's theorem to approximate the solutions to

and give a bound on the error

I computed the 4th degree Taylor polynomial,

of the right hand side at x=0. I reasoned that the intersection must occur when

, so I bounded the error between the Taylor polynomial and the function within

.

Then I computed the intersection between

and

and between

and

. So the solution to the original problem must be between these values. So I took the average of the values as the approximation and half the difference as the bounds for the error...

How does this look? I just ask because my answer had a square root within a square root, and this feels like it is as difficult to approximate as the answer to the original question.

Thanks.