What is the limit as x approaches-7+of sqrt(1/(x+7)) ?

The limit as x approaches-7+of sqrt(1/(x+7)) is infinity

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limit as x approaches-7+of sqrt(1/(x+7))

x \to - 7 + lim (\frac{1}{x + 7})

\infty

Solution steps

x \to - 7 + lim (\frac{1}{x + 7})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= x \to - 7 + lim (\frac{1}{x + 7})

For

x

approaching

- 7

from the right

, x > - 7 \Rightarrow x + 7 > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

Apply Infinity Property:

\infty^{c} = \infty

= \infty

\int_{2}^{4} 3 e^{3 x} d x

\frac{d}{d x} (6 e^{x})

x \to 1 lim (3 x + 1)

\int x (ln (x))^{3} d x

\int \frac{e ^{3 x}}{1 + e ^{x}} d x

What is the limit as x approaches-7+of sqrt(1/(x+7)) ?
The limit as x approaches-7+of sqrt(1/(x+7)) is infinity