Calculus Examples

$\frac{lim_{h \to 0} {(e^{2 + h} - e)}^{2}}{h}$

Step 1

Evaluate the limit.

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Step 1.1

Move the exponent $2$ from ${(e^{2 + h} - e)}^{2}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{h \to 0} e^{2 + h} - e)}^{2}}{h}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $h$ approaches $0$ .

$\frac{{(lim_{h \to 0} e^{2 + h} - lim_{h \to 0} e)}^{2}}{h}$

Step 1.3

Move the limit into the exponent.

$\frac{{(e^{lim_{h \to 0} 2 + h} - lim_{h \to 0} e)}^{2}}{h}$

Step 1.4

Split the limit using the Sum of Limits Rule on the limit as $h$ approaches $0$ .

$\frac{{(e^{lim_{h \to 0} 2 + lim_{h \to 0} h} - lim_{h \to 0} e)}^{2}}{h}$

Step 1.5

Evaluate the limit of $2$ which is constant as $h$ approaches $0$ .

$\frac{{(e^{2 + lim_{h \to 0} h} - lim_{h \to 0} e)}^{2}}{h}$

Step 1.6

Evaluate the limit of $e$ which is constant as $h$ approaches $0$ .

$\frac{{(e^{2 + lim_{h \to 0} h} - e)}^{2}}{h}$

Step 2

Evaluate the limit of $h$ by plugging in $0$ for $h$ .

$\frac{{(e^{2 + 0} - e)}^{2}}{h}$

Step 3

Add $2$ and $0$ .

$\frac{{(e^{2} - e)}^{2}}{h}$