Calculus Examples

$\frac{lim_{h \to 0} e^{5 + h} - e^{5}}{h}$

Step 1

Evaluate the limit.

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Step 1.1

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

$\frac{lim_{h \to 0} e^{5 + h} - lim_{h \to 0} e^{5}}{h}$

Step 1.2

Move the limit into the exponent.

$\frac{e^{lim_{h \to 0} 5 + h} - lim_{h \to 0} e^{5}}{h}$

Step 1.3

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

$\frac{e^{lim_{h \to 0} 5 + lim_{h \to 0} h} - lim_{h \to 0} e^{5}}{h}$

Step 1.4

Evaluate the limit of $5$ which is constant as $h$ approaches $0$ .

$\frac{e^{5 + lim_{h \to 0} h} - lim_{h \to 0} e^{5}}{h}$

Step 1.5

Evaluate the limit of $e^{5}$ which is constant as $h$ approaches $0$ .

$\frac{e^{5 + lim_{h \to 0} h} - e^{5}}{h}$

Step 2

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

$\frac{e^{5 + 0} - e^{5}}{h}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Add $5$ and $0$ .

$\frac{e^{5} - e^{5}}{h}$

Step 3.1.2

Subtract $e^{5}$ from $e^{5}$ .

$\frac{0}{h}$

Step 3.2

Divide $0$ by $h$ .

$0$