Calculus Examples

$\frac{lim_{x \to 8} x + x^{2}}{9 - 2 x^{2}}$

Step 1

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

$\frac{lim_{x \to 8} x + lim_{x \to 8} x^{2}}{9 - 2 x^{2}}$

Step 2

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

$\frac{lim_{x \to 8} x + {(lim_{x \to 8} x)}^{2}}{9 - 2 x^{2}}$

Step 3

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

Tap for more steps...

Step 3.1

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

$\frac{8 + {(lim_{x \to 8} x)}^{2}}{9 - 2 x^{2}}$

Step 3.2

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

$\frac{8 + 8^{2}}{9 - 2 x^{2}}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

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

$\frac{8 + 64}{9 - 2 x^{2}}$

Step 4.2

Add $8$ and $64$ .

$\frac{72}{9 - 2 x^{2}}$