Consider the function f(x) = e. We want to show that f'(x) = e. Here is what you can use for this problem: Everything we proved about the derivative and limits. The following definition for the exponential function: e Σ . n=0 ⚫Common exponentiation rules, such as ea+b= e.eb. • e = 1. (a) Show that f'(0) = 1. (b) Find limo and prove your answer. (c) Using the definition of the derivative, show that f'(x) = e.
Consider the function f(x) = e. We want to show that f'(x) = e. Here is what you can use for this problem: Everything we proved about the derivative and limits. The following definition for the exponential function: e Σ . n=0 ⚫Common exponentiation rules, such as ea+b= e.eb. • e = 1. (a) Show that f'(0) = 1. (b) Find limo and prove your answer. (c) Using the definition of the derivative, show that f'(x) = e.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the function f(x) = e. We want to show that f'(x) = e. Here
is what you can use for this problem:
Everything we proved about the derivative and limits.
The following definition for the exponential function:
e
Σ
.
n=0
⚫Common exponentiation rules, such as ea+b= e.eb.
• e = 1.
(a) Show that f'(0) = 1.
(b) Find limo and prove your answer.
(c) Using the definition of the derivative, show that f'(x) = e.
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