Calculus Examples

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

Step 1

Convert from $\frac{1}{\sin (\frac{1}{x})}$ to $\csc (\frac{1}{x})$ .

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

Step 2

Evaluate the limit.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 3

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

$\csc (\frac{1}{8})$

Step 4

Evaluate $\csc (\frac{1}{8})$ .

$8.02087137$