Question

Below, we use the definition of the derivative to find $f'(x)$ when $f(x) = \frac{5}{x}$. Fill in the blanks. $\lim_{h \to 0} \left( \frac{f(x+h) - f(x)}{h} \right)$ $= \lim_{h \to 0} \frac{\text{_____}}{h} - \frac{5}{x}$ $= \lim_{h \to 0} \frac{5x - 5(x+h)}{h}$ $= \lim_{h \to 0} \left( \frac{5x - 5x - 5h}{(x+h)xh} \right)$ $= \lim_{h \to 0} \left( \frac{-5h}{(x+h)xh} \right)$ $= \text{_____}$

          Below, we use the definition of the derivative to find $f'(x)$ when $f(x) = \frac{5}{x}$.
Fill in the blanks.
$\lim_{h \to 0} \left( \frac{f(x+h) - f(x)}{h} \right)$
$= \lim_{h \to 0} \frac{\text{_____}}{h} - \frac{5}{x}$
$= \lim_{h \to 0} \frac{5x - 5(x+h)}{h}$
$= \lim_{h \to 0} \left( \frac{5x - 5x - 5h}{(x+h)xh} \right)$
$= \lim_{h \to 0} \left( \frac{-5h}{(x+h)xh} \right)$
$= \text{_____}$

Below, we use the definition of the derivative to find f'(x) when f(x) = (5)/(x).
Fill in the blanks.
limh → 0( (f(x+h) - f(x))/(h))
= limh → 0()/(h) - (5)/(x)
= limh → 0(5x - 5(x+h))/(h)
= limh → 0( (5x - 5x - 5h)/((x+h)xh))
= limh → 0( (-5h)/((x+h)xh))
=

Added by Steven N.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

07/07/2023

Step 1

Step 1: Using the definition of the derivative, we have f^'() = lim h->0 [f(x+h) - f(x)] / h. Show more…

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Below, we use the definition of the derivative to find f^(')(x) when f(x)=(5)/(x). Fill in the blanks.end{array}] 5 x Below, we use the definition of the derivative to find f'() when f() Fill in the blanks. f(x+h)-f(x) lim h>0 h 5 x lim h->0 h 5x-5(x+h) lim h >0 h 5x- 5x - 5h lim h->0 (x+h)xh -5h lim h->0 x+h)xh