Calculus Examples

$lim_{x \to 1} \ln (3 x^{2} + 4)$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the logarithm.

$\ln (lim_{x \to 1} 3 x^{2} + 4)$

Step 1.2

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

$\ln (lim_{x \to 1} 3 x^{2} + lim_{x \to 1} 4)$

Step 1.3

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

$\ln (3 lim_{x \to 1} x^{2} + lim_{x \to 1} 4)$

Step 1.4

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$\ln (3 {(lim_{x \to 1} x)}^{2} + lim_{x \to 1} 4)$

Step 1.5

Evaluate the limit of $4$ which is constant as $x$ approaches $1$ .

$\ln (3 {(lim_{x \to 1} x)}^{2} + 4)$

Step 2

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

$\ln (3 \cdot 1^{2} + 4)$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

One to any power is one.

$\ln (3 \cdot 1 + 4)$

Step 3.1.2

Multiply $3$ by $1$ .

$\ln (3 + 4)$

Step 3.2

Add $3$ and $4$ .

$\ln (7)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\ln (7)$

Decimal Form:

$1.94591014 \dots$