Calculus Examples

$lim_{x \to 8} \frac{1}{x} \cdot \sin (x)$

Step 1

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

$lim_{x \to 8} \frac{1}{x} \cdot lim_{x \to 8} \sin (x)$

Step 2

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

$\frac{lim_{x \to 8} 1}{lim_{x \to 8} x} \cdot lim_{x \to 8} \sin (x)$

Step 3

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

$\frac{1}{lim_{x \to 8} x} \cdot lim_{x \to 8} \sin (x)$

Step 4

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

$\frac{1}{lim_{x \to 8} x} \cdot \sin (lim_{x \to 8} x)$

Step 5

Evaluate the limits by plugging in $8$ for all occurrences of $x$ .

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Step 5.1

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

$\frac{1}{8} \cdot \sin (lim_{x \to 8} x)$

Step 5.2

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

$\frac{1}{8} \cdot \sin (8)$

Step 6

Simplify the answer.

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Step 6.1

Evaluate $\sin (8)$ .

$\frac{1}{8} \cdot 0.1391731$

Step 6.2

Combine $\frac{1}{8}$ and $0.1391731$ .

$\frac{0.1391731}{8}$

Step 6.3

Divide $0.1391731$ by $8$ .

$0.01739663$