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Problem 2

(a) Sketch, by hand, the graph of the function $ …

02:37
Problem 2

(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?
Problem 3

Differentiate the function.
$ f(x) = 2^{40} $
Problem 4

Differentiate the function.
$ f(x) = e^5 $
Problem 5

Differentiate the function.
$ f(x) = 5.2x + 2.3 $
Problem 6

Differentiate the function.
$ g(x) = \frac{7}{4}x^2 - 3x + 12 $
Clarissa N.
Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86

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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 $0.99<1<1.03,2.7<e<2.8$

More Answers
Frank L.
01:34
Chapter 3
Differentiation Rules
Section 1
Derivatives of Polynomials and Exponential Functions
Calculus: Early Transcendentals

Topics

Derivatives of Polynomials and Exponential Functions

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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

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