Calculus Examples

$lim_{x \to 0.785} \frac{4 x}{\tan (x)}$

Step 1

Move the term $4$ outside of the limit because it is constant with respect to $x$ .

$4 lim_{x \to 0.785} \frac{x}{\tan (x)}$

Step 2

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $0.785$ .

$4 \frac{lim_{x \to 0.785} x}{lim_{x \to 0.785} \tan (x)}$

Step 3

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

$4 \frac{lim_{x \to 0.785} x}{\tan (lim_{x \to 0.785} x)}$

Step 4

Evaluate the limits by plugging in $0.785$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $0.785$ for $x$ .

$4 \frac{0.785}{\tan (lim_{x \to 0.785} x)}$

Step 4.2

Evaluate the limit of $x$ by plugging in $0.785$ for $x$ .

$4 \frac{0.785}{\tan (0.785)}$

Step 5

Simplify the answer.

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Step 5.1

Separate fractions.

$4 (\frac{0.785}{1} \cdot \frac{1}{\tan (0.785)})$

Step 5.2

Rewrite $\tan (0.785)$ in terms of sines and cosines.

$4 (\frac{0.785}{1} \cdot \frac{1}{\frac{\sin (0.785)}{\cos (0.785)}})$

Step 5.3

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (0.785)}{\cos (0.785)}$ .

$4 (\frac{0.785}{1} \cdot \frac{\cos (0.785)}{\sin (0.785)})$

Step 5.4

Convert from $\frac{\cos (0.785)}{\sin (0.785)}$ to $\cot (0.785)$ .

$4 (\frac{0.785}{1} \cot (0.785))$

Step 5.5

Divide $0.785$ by $1$ .

$4 (0.785 \cot (0.785))$

Step 5.6

Multiply $0.785$ by $\cot (0.785)$ .

$4 \cdot 0.78562536$

Step 5.7

Multiply $4$ by $0.78562536$ .

$3.14250146$