Calculus Examples

$\frac{lim_{h \to 0} {2.7}^{h} - 1}{h}$

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 $0$ .

$\frac{lim_{h \to 0} {2.7}^{h} - lim_{h \to 0} 1}{h}$

Step 1.2

Move the limit into the exponent.

$\frac{{2.7}^{lim_{h \to 0} h} - lim_{h \to 0} 1}{h}$

Step 1.3

Evaluate the limit of $1$ which is constant as $h$ approaches $0$ .

$\frac{{2.7}^{lim_{h \to 0} h} - 1 \cdot 1}{h}$

Step 2

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

$\frac{{2.7}^{0} - 1 \cdot 1}{h}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Anything raised to $0$ is $1$ .

$\frac{1 - 1 \cdot 1}{h}$

Step 3.1.2

Multiply $- 1$ by $1$ .

$\frac{1 - 1}{h}$

Step 3.1.3

Subtract $1$ from $1$ .

$\frac{0}{h}$

Step 3.2

Divide $0$ by $h$ .

$0$