What is the limit as x approaches 4-of-1/(x^2-16) ?

The limit as x approaches 4-of-1/(x^2-16) is infinity

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limit as x approaches 4-of-1/(x^2-16)

x \to 4 - lim (- \frac{1}{x ^{2} - 16})

\infty

Solution steps

x \to 4 - lim (- \frac{1}{x ^{2} - 16})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - x \to 4 - lim (\frac{1}{x ^{2} - 16})

For

x

approaching

4

from the left

, x < 4 \Rightarrow x^{2} - 16 < 0

The denominator is a negative quantity approaching 0 from the left

= - (- \infty)

Simplify

= \infty

x \to 0 lim (x + \frac{x}{x ^{2}})

x \to 0 lim (\frac{( x - 2 )}{x ^{4}})

x \to 2 lim (\frac{[ x ]}{x})

x \to 1 lim (3 x^{2} + 4 x)

x \to 0 lim (\frac{e ^{t x} - 1}{x})

What is the limit as x approaches 4-of-1/(x^2-16) ?
The limit as x approaches 4-of-1/(x^2-16) is infinity