Calculus Examples

$lim_{x \to - 8} - 3 x^{16} + 2$

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 $- 8$ .

$- lim_{x \to - 8} 3 x^{16} + lim_{x \to - 8} 2$

Step 1.2

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

$- 3 lim_{x \to - 8} x^{16} + lim_{x \to - 8} 2$

Step 1.3

Move the exponent $16$ from $x^{16}$ outside the limit using the Limits Power Rule.

$- 3 {(lim_{x \to - 8} x)}^{16} + lim_{x \to - 8} 2$

Step 1.4

Evaluate the limit of $2$ which is constant as $x$ approaches $- 8$ .

$- 3 {(lim_{x \to - 8} x)}^{16} + 2$

Step 2

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

$- 3 {(- 8)}^{16} + 2$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Raise $- 8$ to the power of $16$ .

$- 3 \cdot 281474976710656 + 2$

Step 3.1.2

Multiply $- 3$ by $281474976710656$ .

$- 844424930131968 + 2$

Step 3.2

Add $- 844424930131968$ and $2$ .

$- 844424930131966$