Calculus Examples

$lim_{x \to 3} \frac{{(x - 3)}^{4}}{{(x - 3)}^{5}}$

Step 1

Cancel the common factor of ${(x - 3)}^{4}$ and ${(x - 3)}^{5}$ .

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Step 1.1

Multiply by $1$ .

$lim_{x \to 3} \frac{{(x - 3)}^{4} \cdot 1}{{(x - 3)}^{5}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor ${(x - 3)}^{4}$ out of ${(x - 3)}^{5}$ .

$lim_{x \to 3} \frac{{(x - 3)}^{4} \cdot 1}{{(x - 3)}^{4} (x - 3)}$

Step 1.2.2

Cancel the common factor.

$lim_{x \to 3} \frac{{(x - 3)}^{4} \cdot 1}{{(x - 3)}^{4} (x - 3)}$

Step 1.2.3

Rewrite the expression.

$lim_{x \to 3} \frac{1}{x - 3}$

Step 2

Since the function approaches $- \infty$ from the left and $\infty$ from the right, the limit does not exist.

$Does not exist$