Calculus Examples

$lim_{x \to 1} \ln (3 x + e^{x})$

Step 1

Move the limit inside the logarithm.

$\ln (lim_{x \to 1} 3 x + e^{x})$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$\ln (lim_{x \to 1} 3 x + lim_{x \to 1} e^{x})$

Step 3

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$\ln (3 lim_{x \to 1} x + lim_{x \to 1} e^{x})$

Step 4

Move the limit into the exponent.

$\ln (3 lim_{x \to 1} x + e^{lim_{x \to 1} x})$

Step 5

Evaluate the limits by plugging in $1$ for all occurrences of $x$ .

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Step 5.1

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\ln (3 \cdot 1 + e^{lim_{x \to 1} x})$

Step 5.2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\ln (3 \cdot 1 + e^{1})$

Step 6

Simplify each term.

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Step 6.1

Multiply $3$ by $1$ .

$\ln (3 + e^{1})$

Step 6.2

Simplify.

$\ln (3 + e)$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\ln (3 + e)$

Decimal Form:

$1.74366838 \dots$