Calculus Examples

$lim_{x \to - 8} \sqrt{x^{2} + 3 + x}$

Step 1

Move the limit under the radical sign.

$\sqrt{lim_{x \to - 8} x^{2} + 3 + x}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 8$ .

$\sqrt{lim_{x \to - 8} x^{2} + lim_{x \to - 8} 3 + lim_{x \to - 8} x}$

Step 3

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

$\sqrt{{(lim_{x \to - 8} x)}^{2} + lim_{x \to - 8} 3 + lim_{x \to - 8} x}$

Step 4

Evaluate the limit of $3$ which is constant as $x$ approaches $- 8$ .

$\sqrt{{(lim_{x \to - 8} x)}^{2} + 3 + lim_{x \to - 8} x}$

Step 5

Evaluate the limits by plugging in $- 8$ for all occurrences of $x$ .

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Step 5.1

Evaluate the limit of $x$ by plugging in $- 8$ for $x$ .

$\sqrt{{(- 8)}^{2} + 3 + lim_{x \to - 8} x}$

Step 5.2

Evaluate the limit of $x$ by plugging in $- 8$ for $x$ .

$\sqrt{{(- 8)}^{2} + 3 - 8}$

Step 6

Simplify the answer.

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Step 6.1

Raise $- 8$ to the power of $2$ .

$\sqrt{64 + 3 - 8}$

Step 6.2

Add $64$ and $3$ .

$\sqrt{67 - 8}$

Step 6.3

Subtract $8$ from $67$ .

$\sqrt{59}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\sqrt{59}$

Decimal Form:

$7.68114574 \dots$