1. IEEE floating point arithmetic

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?

2. Originally Posted by PvtBillPilgrim
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?
You want the largest $x$ such that:

$\exp(-2x^2)=1$

to IEEE double pressicion. Well this is a small value so we may as well write (this where the Maclaurin series comes in):

$-2x^2=0$

to IEEE double prescission, so:

$2 x^2<\text{eps}$

or $x<\sqrt{\frac{\text{eps}}{2}}$

CB