Question

Match the given limit with a derivative, then find the limit by computing the derivative.

lim ((h+3)^3-27)/h
h->0

part 1) what is the derivative that matches the given limit?
f'(x)=

Answer 1

\[\lim_{h \rightarrow 0}\frac{ \left( h+3 \right)^3-27 }{ h }=\lim_{h \rightarrow 0}\frac{ h^3+3h^2*3+3h*3^2 +27-27 }{ h }\]
\[=\lim_{h \rightarrow 0}\frac{ h \left( h^2+9h+27 \right) }{ h }=?\]
\[\lim_{h \rightarrow 0}\frac{ \left( h+3 \right)^3-27 }{ h }=\lim_{h \rightarrow 0}\frac{ 3\left( h+3 \right) ^2}{ 1 }=?\]