Question

10. Use CAUCHY's definition of the derivative to prove that, if $f(x) = e^x$, then $f'(x) = e^x$. [HINT: You may want to use the fact that, as $h \rightarrow 0, e^h \rightarrow 1 + h$.]

Name: 10 use cauchys definition of the derivative to prove that if fx ex then fx ex hint you may want to use the fact that as h rightarrow 0 eh rightarrow 1 h 24577
Uploaded: 2023-03-14T09:42:19-08:00
Duration: 2 min 34 s
Channel: Supreeta N
Description: 10 use cauchys definition of the derivative to prove that if fx ex then fx ex hint you may want to use the fact that as h rightarrow 0 eh rightarrow 1 h 24577

          10. Use CAUCHY's definition of the derivative to prove that, if $f(x) = e^x$, then $f'(x) = e^x$.
[HINT: You may want to use the fact that, as $h \rightarrow 0, e^h \rightarrow 1 + h$.]

10 use cauchys definition of the derivative to prove that if fx ex then fx ex hint you may want to use the fact that as h rightarrow 0 eh rightarrow 1 h 24577

Added by Lisa F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

03/14/2023

Step 1

Cauchy's definition of the derivative is given by: $$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$ Show more…

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10. Use CAUCHY's definition of the derivative to prove that, if $f(x) = e^x$, then $f'(x) = e^x$. [HINT: You may want to use the fact that, as $h \rightarrow 0, e^h \rightarrow 1 + h$.]