Absolute and relative uncertainties of functions can behave in nonintuitive ways. Let y = e x

.

a. Calculate the absolute uncertainty of y in terms of the absolute uncertainty of x. What happens as x gets large and negative? Explain why this makes sense.

Hint: plot the graph of y(x). What does this graph do as x → −∞ and how does this relate to the absolute error?

b. Now calculate the relative uncertainty of y as a function of the relative uncertainty of x. How do these two relative uncertainties compare as x → −∞? Again, explain why this makes sense.