Checkpoint 3

1. Use the pop-up calculator, with a 16-digit calculation, to evaluate the expression `sqrt(x^2+1)-x` at `x=42text[,]709`. The correct answer, to 16 significant digits, is `1.1707134326054731 times 10^(-5)`. How many digits of your answer are significant?
2. Evaluate the same expression at `x=1text[,]342text[,]709`, again with a 16-digit calculation. The correct answer, to 16 significant digits, is `3.723815063427226 times 10^(-7)`. How many digits of your answer are significant?

To see how to get better approximations — that is, how to avoid the disastrous cancellations that arise from this subtraction of nearly equal numbers — do Exercise 5 at the end of the section.