What is the limit as h approaches 3 of (3(x+h)^3-3x^3)/h ?

The limit as h approaches 3 of (3(x+h)^3-3x^3)/h is (x+3)^3-x^3

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limit as h approaches 3 of (3(x+h)^3-3x^3)/h

h \to 3 lim (\frac{3 ( x + h ) ^{3} - 3 x ^{3}}{h})

(x + 3)^{3} - x^{3}

Solution steps

h \to 3 lim (\frac{3 ( x + h ) ^{3} - 3 x ^{3}}{h})

Plug in the value

h = 3

= \frac{3 ( x + 3 ) ^{3} - 3 x ^{3}}{3}

Simplify

\frac{3 ( x + 3 ) ^{3} - 3 x ^{3}}{3} : (x + 3)^{3} - x^{3}

= (x + 3)^{3} - x^{3}

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What is the limit as h approaches 3 of (3(x+h)^3-3x^3)/h ?
The limit as h approaches 3 of (3(x+h)^3-3x^3)/h is (x+3)^3-x^3