Calculus Examples

$lim_{x \to 8} 7 \cos (\frac{7}{3 x})$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $7$ outside of the limit because it is constant with respect to $x$ .

$7 lim_{x \to 8} \cos (\frac{7}{3 x})$

Step 1.2

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

$7 \cos (lim_{x \to 8} \frac{7}{3 x})$

Step 1.3

Move the term $\frac{7}{3}$ outside of the limit because it is constant with respect to $x$ .

$7 \cos (\frac{7}{3} lim_{x \to 8} \frac{1}{x})$

Step 1.4

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $8$ .

$7 \cos (\frac{7}{3} \cdot \frac{lim_{x \to 8} 1}{lim_{x \to 8} x})$

Step 1.5

Evaluate the limit of $1$ which is constant as $x$ approaches $8$ .

$7 \cos (\frac{7}{3} \cdot \frac{1}{lim_{x \to 8} x})$

Step 2

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

$7 \cos (\frac{7}{3} \cdot \frac{1}{8})$

Step 3

Simplify the answer.

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Step 3.1

Multiply $\frac{7}{3} \cdot \frac{1}{8}$ .

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Step 3.1.1

Multiply $\frac{7}{3}$ by $\frac{1}{8}$ .

$7 \cos (\frac{7}{3 \cdot 8})$

Step 3.1.2

Multiply $3$ by $8$ .

$7 \cos (\frac{7}{24})$

Step 3.2

Evaluate $\cos (\frac{7}{24})$ .

$7 \cdot 0.95776595$

Step 3.3

Multiply $7$ by $0.95776595$ .

$6.7043617$