Calculus Examples

$\frac{lim_{x \to - 1} x^{2 (2 x) + 1}}{x^{2} - 3 x - 4}$

Step 1

Multiply $2$ by $2$ .

$\frac{lim_{x \to - 1} x^{4 x + 1}}{x^{2} - 3 x - 4}$

Step 2

Use the properties of logarithms to simplify the limit.

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Step 2.1

Rewrite $x^{4 x + 1}$ as $e^{\ln (x^{4 x + 1})}$ .

$\frac{lim_{x \to - 1} e^{\ln (x^{4 x + 1})}}{x^{2} - 3 x - 4}$

Step 2.2

Expand $\ln (x^{4 x + 1})$ by moving $4 x + 1$ outside the logarithm.

$\frac{lim_{x \to - 1} e^{(4 x + 1) \ln (x)}}{x^{2} - 3 x - 4}$

Step 3

Since the values of $e^{(4 x + 1) \ln (x)}$ do not exist on either side of $- 1$ , the limit does not exist.

$\frac{Does not exist}{x^{2} - 3 x - 4}$

Step 4

The limit does not exist.

$Does not exist$