Calculus Examples

$lim_{x \to 0} 2 \sin (x) - 1$

Step 1

Evaluate the limit.

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Step 1.1

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

$lim_{x \to 0} 2 \sin (x) - lim_{x \to 0} 1$

Step 1.2

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$2 lim_{x \to 0} \sin (x) - lim_{x \to 0} 1$

Step 1.3

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

$2 \sin (lim_{x \to 0} x) - lim_{x \to 0} 1$

Step 1.4

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

$2 \sin (lim_{x \to 0} x) - 1 \cdot 1$

Step 2

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

$2 \sin (0) - 1 \cdot 1$

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 $\sin (0)$ is $0$ .

$2 \cdot 0 - 1 \cdot 1$

Step 3.1.2

Multiply $2$ by $0$ .

$0 - 1 \cdot 1$

Step 3.1.3

Multiply $- 1$ by $1$ .

$0 - 1$

Step 3.2

Subtract $1$ from $0$ .

$- 1$