Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the limit under the radical sign.

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

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

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

Step 1.3

Evaluate the limit of $3$ which is constant as $x$ approaches $1$ .

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

Step 2

Evaluate the limit of $f (x)$ by plugging in $1$ for $x$ .

$\sqrt{3 + f (1)}$