Calculus Examples

$\frac{lim_{x \to 8} \tan (12 x^{2})}{\ln (1 + 4 x^{2})}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit inside the trig function because tangent is continuous.

$\frac{\tan (lim_{x \to 8} 12 x^{2})}{\ln (1 + 4 x^{2})}$

Step 1.2

Move the term $12$ outside of the limit because it is constant with respect to $x$ .

$\frac{\tan (12 lim_{x \to 8} x^{2})}{\ln (1 + 4 x^{2})}$

Step 1.3

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

$\frac{\tan (12 {(lim_{x \to 8} x)}^{2})}{\ln (1 + 4 x^{2})}$

Step 2

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$\frac{\tan (12 \cdot 8^{2})}{\ln (1 + 4 x^{2})}$

Step 3

Simplify the numerator.

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Step 3.1

Raise $8$ to the power of $2$ .

$\frac{\tan (12 \cdot 64)}{\ln (1 + 4 x^{2})}$

Step 3.2

Multiply $12$ by $64$ .

$\frac{\tan (768)}{\ln (1 + 4 x^{2})}$

Step 3.3

Remove full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$\frac{\tan (48)}{\ln (1 + 4 x^{2})}$

Step 3.4

Evaluate $\tan (48)$ .

$\frac{1.11061251}{\ln (1 + 4 x^{2})}$