Calculus Examples

$lim_{x \to 2} 3 f {(x)}^{2} + g (x)$

Step 1

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

$lim_{x \to 2} 3 f {(x)}^{2} + lim_{x \to 2} g (x)$

Step 2

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

$3 f lim_{x \to 2} {(x)}^{2} + lim_{x \to 2} g (x)$

Step 3

Move the exponent $2$ from ${(x)}^{2}$ outside the limit using the Limits Power Rule.

$3 f {(lim_{x \to 2} x)}^{2} + lim_{x \to 2} g (x)$

Step 4

Evaluate the limits by plugging in $2$ for all occurrences of $x$ .

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Step 4.1

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

$3 f \cdot 2^{2} + lim_{x \to 2} g (x)$

Step 4.2

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

$3 f \cdot 2^{2} + g (2)$

Step 5

Simplify each term.

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Step 5.1

Raise $2$ to the power of $2$ .

$3 f \cdot 4 + g (2)$

Step 5.2

Multiply $4$ by $3$ .

$12 f + g (2)$