Calculus Examples

$lim_{x \to 2} \sin (\sqrt{3 x + 1})$

Step 1

Evaluate the limit.

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Step 1.1

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

$\sin (lim_{x \to 2} \sqrt{3 x + 1})$

Step 1.2

Move the limit under the radical sign.

$\sin (\sqrt{lim_{x \to 2} 3 x + 1})$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$\sin (\sqrt{lim_{x \to 2} 3 x + lim_{x \to 2} 1})$

Step 1.4

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

$\sin (\sqrt{3 lim_{x \to 2} x + lim_{x \to 2} 1})$

Step 1.5

Evaluate the limit of $1$ which is constant as $x$ approaches $2$ .

$\sin (\sqrt{3 lim_{x \to 2} x + 1})$

Step 2

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\sin (\sqrt{3 \cdot 2 + 1})$

Step 3

Simplify the answer.

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Step 3.1

Multiply $3$ by $2$ .

$\sin (\sqrt{6 + 1})$

Step 3.2

Add $6$ and $1$ .

$\sin (\sqrt{7})$

Step 3.3

Evaluate $\sin (\sqrt{7})$ .

$0.47577183$