Find the limit, if it exists.
-$\lim _ { h \rightarrow 0 } \frac { ( x + h ) ^ { 3 } - x ^ { 3 } } { h }$
A) Does not exist
B) 0
C) $3 x ^ { 2 }$
D) $3 x ^ { 2 } + 3 x h + h ^ { 2 }$

Question

Quizplus · Accepted Answer

This is the limit definition of the derivative of $x^3$. Taking the derivative of $x^3$ gives $3x^2$, so the limit is $\boxed{	extbf{(C)}\ 3x^2}$.

Find the Limit, If It Exists lim⁡h→0(x+h)3−x3h\lim _ { h \rightarrow 0 } \frac { ( x + h ) ^ { 3 } - x ^ { 3 } } { h }limh→0​h(x+h)3−x3​

Find the Limit, If It Exists $\lim _ { h \rightarrow 0 } \frac { ( x + h ) ^ { 3 } - x ^ { 3 } } { h }$