Calculus Examples

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

Step 1

Move the exponent $2 - 49$ from $x^{2 - 49}$ outside the limit using the Limits Power Rule.

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

Step 2

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

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

Step 3

Simplify the answer.

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Step 3.1

Move $7^{2 - 49}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3.2

Simplify the denominator.

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Step 3.2.1

Subtract $49$ from $2$ .

$\frac{1}{(x - 7) \cdot 7^{- - 47}}$

Step 3.2.2

Multiply $- 1$ by $- 47$ .

$\frac{1}{(x - 7) \cdot 7^{47}}$

Step 3.3

Reorder factors in $\frac{1}{(x - 7) \cdot 7^{47}}$ .

$\frac{1}{7^{47} (x - 7)}$