Calculus Examples

$lim_{x \to 0} 3 (1 - \cos (x))$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$3 lim_{x \to 0} 1 - \cos (x)$

Step 1.2

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

$3 (lim_{x \to 0} 1 - lim_{x \to 0} \cos (x))$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $0$ .

$3 (1 - lim_{x \to 0} \cos (x))$

Step 1.4

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

$3 (1 - \cos (lim_{x \to 0} x))$

Step 2

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

$3 (1 - \cos (0))$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

$3 (1 - 1 \cdot 1)$

Step 3.1.2

Multiply $- 1$ by $1$ .

$3 (1 - 1)$

Step 3.2

Subtract $1$ from $1$ .

$3 \cdot 0$

Step 3.3

Multiply $3$ by $0$ .

$0$