(a) Sketch, by hand, the graph of the function $ f(x) = e^x, $ paying particular attention to the graph crosses the y-axes.
What fact allows you to do this?
(b) What types of functions are $ f(x) = e^x $ and $ g(x) = x^e? $
Compare the differentiation formulas for $ f $ and $ g. $
(c) Which of the two functions in part (b) grows more rapidly when $ x $ is large?
hands Claire's when you read here. So he has a number such that the limit. Those beach approaches. Zero. You have a TSH minus one. Oh, her h This vehicle to one for part B. We have the limit using a calculator. Each approaches infinity 2.7 to the H power minus one over age is equivalent to a 0.99 The limit as each approaches infinity 2.8 to the H power minus one or her age is equivalent two 1.3 And you know that E is a number such that the slope of e of X is one at X equals zero and we also know the formula limit. Each approaches infinity. Many of beach minus one for her h is equal to the derivative. So he sought that the slope of A of X for a is equal to 2.7. It's less than one, and for a is equal to 2.8 is more than one. So it has to be between, um, 2.7 92.8 since the slope of A to X power when a equals E is one