Calculus Examples

$lim_{x \to 0} 2^{x} + 3^{x} + 16 x$

Step 1

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

$lim_{x \to 0} 2^{x} + lim_{x \to 0} 3^{x} + lim_{x \to 0} 16 x$

Step 2

Move the limit into the exponent.

$2^{lim_{x \to 0} x} + lim_{x \to 0} 3^{x} + lim_{x \to 0} 16 x$

Step 3

Move the limit into the exponent.

$2^{lim_{x \to 0} x} + 3^{lim_{x \to 0} x} + lim_{x \to 0} 16 x$

Step 4

Move the term $16$ outside of the limit because it is constant with respect to $x$ .

$2^{lim_{x \to 0} x} + 3^{lim_{x \to 0} x} + 16 lim_{x \to 0} x$

Step 5

Evaluate the limits by plugging in $0$ for all occurrences of $x$ .

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Step 5.1

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

$2^{0} + 3^{lim_{x \to 0} x} + 16 lim_{x \to 0} x$

Step 5.2

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

$2^{0} + 3^{0} + 16 lim_{x \to 0} x$

Step 5.3

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

$2^{0} + 3^{0} + 16 \cdot 0$

Step 6

Simplify the answer.

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Step 6.1

Simplify each term.

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Step 6.1.1

Anything raised to $0$ is $1$ .

$1 + 3^{0} + 16 \cdot 0$

Step 6.1.2

Anything raised to $0$ is $1$ .

$1 + 1 + 16 \cdot 0$

Step 6.1.3

Multiply $16$ by $0$ .

$1 + 1 + 0$

Step 6.2

Add $1$ and $1$ .

$2 + 0$

Step 6.3

Add $2$ and $0$ .

$2$