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

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

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

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

\infty

Solution steps

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

For

x

approaching

- 4

from the left

, x < - 4 \Rightarrow (x + 4)^{2} > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

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

x \to 0 lim (\frac{x ^{2}}{x ^{2} - 9})

x \to 0 lim ((1 + x)^{- \frac{3}{x}})

x \to 1 lim (\frac{2}{x})

x \to - \infty lim (- 1 x)

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