Calculus Examples

$\frac{lim_{x \to 10} x^{2} + 100}{x - 10}$

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 $10$ .

$\frac{lim_{x \to 10} x^{2} + lim_{x \to 10} 100}{x - 10}$

Step 1.2

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

$\frac{{(lim_{x \to 10} x)}^{2} + lim_{x \to 10} 100}{x - 10}$

Step 1.3

Evaluate the limit of $100$ which is constant as $x$ approaches $10$ .

$\frac{{(lim_{x \to 10} x)}^{2} + 100}{x - 10}$

Step 2

Evaluate the limit of $x$ by plugging in $10$ for $x$ .

$\frac{10^{2} + 100}{x - 10}$

Step 3

Simplify the numerator.

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Step 3.1

Raise $10$ to the power of $2$ .

$\frac{100 + 100}{x - 10}$

Step 3.2

Add $100$ and $100$ .

$\frac{200}{x - 10}$