Calculus Examples

$lim_{x \to \ln (10)} e^{x} + 2$

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 $x$ approaches $\ln (10)$ .

$lim_{x \to \ln (10)} e^{x} + lim_{x \to \ln (10)} 2$

Step 1.2

Move the limit into the exponent.

$e^{lim_{x \to \ln (10)} x} + lim_{x \to \ln (10)} 2$

Step 1.3

Evaluate the limit of $2$ which is constant as $x$ approaches $\ln (10)$ .

$e^{lim_{x \to \ln (10)} x} + 2$

Step 2

Evaluate the limit of $x$ by plugging in $\ln (10)$ for $x$ .

$e^{\ln (10)} + 2$

Step 3

Simplify the answer.

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Step 3.1

Exponentiation and log are inverse functions.

$10 + 2$

Step 3.2

Add $10$ and $2$ .

$12$