Enroll in one of our FREE online STEM summer camps. Space is limited so join now!View Summer Courses

### (a) Sketch, by hand, the graph of the function $… 02:37 Need more help? Fill out this quick form to get professional live tutoring. Get live tutoring Problem 1 (a) How is the number$ e $defined? (b) Use a calculator to estimate the values of the limits$ \displaystyle \lim_{h\to 0}\frac {2.7^h - 1}{h} $and$ \displaystyle \lim_{h\to 0}\frac {2.8^h - 1}{h} $correct to two decimal places. What can you conclude about the value of$ e $? Answer a.$\lim _{h \rightarrow 0} \frac{e^{h}-1}{h}=1$b. since$0.99<1<1.03,2.7<e<2.8\$

Frank L.
01:34

Calculus: Early Transcendentals

## Discussion

You must be signed in to discuss.

## Video Transcript

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