Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ for $f ( x ) = 8 - x$.
A) 1
B) 9
C) $- 1$
D) 8
E) limit does not exist

Question

Quizplus · Accepted Answer

\begin{align*}
\lim _ { h ightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } &= \lim _ { h ightarrow 0 } \frac { (8 - (x+h)) - (8-x) } { h } \
&= \lim _ { h ightarrow 0 } \frac { -h } { h } \
&= \lim _ { h ightarrow 0 } -1 \
&= -1
\end{align*}

Find lim⁡h→0f(x+h)−f(x)h\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }limh→0​hf(x+h)−f(x)​

Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$