Calculus Examples

$\frac{lim_{x \to 7} x^{2} - 49}{x - 7}$

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 $7$ .

$\frac{lim_{x \to 7} x^{2} - lim_{x \to 7} 49}{x - 7}$

Step 1.2

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

$\frac{{(lim_{x \to 7} x)}^{2} - lim_{x \to 7} 49}{x - 7}$

Step 1.3

Evaluate the limit of $49$ which is constant as $x$ approaches $7$ .

$\frac{{(lim_{x \to 7} x)}^{2} - 1 \cdot 49}{x - 7}$

Step 2

Evaluate the limit of $x$ by plugging in $7$ for $x$ .

$\frac{7^{2} - 1 \cdot 49}{x - 7}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $7$ to the power of $2$ .

$\frac{49 - 1 \cdot 49}{x - 7}$

Step 3.1.2

Multiply $- 1$ by $49$ .

$\frac{49 - 49}{x - 7}$

Step 3.1.3

Subtract $49$ from $49$ .

$\frac{0}{x - 7}$

Step 3.2

Divide $0$ by $x - 7$ .

$0$