Calculus Examples

$lim_{x \to 0} \cos (7 x)$

Step 1

Evaluate the limit.

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Step 1.1

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

$\cos (lim_{x \to 0} 7 x)$

Step 1.2

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

$\cos (7 lim_{x \to 0} x)$

Step 2

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

$\cos (7 \cdot 0)$

Step 3

Simplify the answer.

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Step 3.1

Multiply $7$ by $0$ .

$\cos (0)$

Step 3.2

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

$1$