Calculus Examples

$lim_{x \to 0} \frac{x}{\cos (x)}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $0$ .

$\frac{lim_{x \to 0} x}{lim_{x \to 0} \cos (x)}$

Step 2

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

$\frac{lim_{x \to 0} x}{\cos (lim_{x \to 0} x)}$

Step 3

Evaluate the limits by plugging in $0$ for all occurrences of $x$ .

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Step 3.1

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\frac{0}{\cos (lim_{x \to 0} x)}$

Step 3.2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\frac{0}{\cos (0)}$

Step 4

Simplify the answer.

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Step 4.1

Separate fractions.

$\frac{0}{1} \cdot \frac{1}{\cos (0)}$

Step 4.2

Convert from $\frac{1}{\cos (0)}$ to $\sec (0)$ .

$\frac{0}{1} \sec (0)$

Step 4.3

Divide $0$ by $1$ .

$0 \sec (0)$

Step 4.4

The exact value of $\sec (0)$ is $1$ .

$0 \cdot 1$

Step 4.5

Multiply $0$ by $1$ .

$0$