Estimate the largest real number x such that 1 - exp(-2x^2) = 0 on a machine using

the IEEE standard for binary double precision floating point arithmetic. (Hint: a Maclaurin series

might be useful.)

What would be this number? Obviously, zero is a solution to the expression, but there must be a positive root somewhere. If not, then it should be zero + eps/2. How do you think you use the Maclaurin series?