What is the limit as x approaches 8+of 1/(x-8)-1/(sqrt(x-8)) ?

The limit as x approaches 8+of 1/(x-8)-1/(sqrt(x-8)) is infinity

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limit as x approaches 8+of 1/(x-8)-1/(sqrt(x-8))

x \to 8 + lim (\frac{1}{x - 8} - \frac{1}{x - 8})

\infty

Solution steps

x \to 8 + lim (\frac{1}{x - 8} - \frac{1}{x - 8})

\frac{1}{x - 8} - \frac{1}{x - 8} = \frac{1}{x - 8} (1 - \frac{\frac{1}{x - 8}}{\frac{1}{x - 8}})

= x \to 8 + lim (\frac{1}{x - 8} (1 - \frac{\frac{1}{x - 8}}{\frac{1}{x - 8}}))

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

With the exception of indeterminate form

= x \to 8 + lim (\frac{1}{x - 8}) \cdot x \to 8 + lim (1 - \frac{\frac{1}{x - 8}}{\frac{1}{x - 8}})

x \to 8 + lim (\frac{1}{x - 8}) = \infty

x \to 8 + lim (1 - \frac{\frac{1}{x - 8}}{\frac{1}{x - 8}}) = 1

= \infty \cdot 1

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 4 lim (\frac{5 + x}{x - 4})

n = 1 \sum \infty \frac{2}{n ^{3}}

\int t 7 t^{2} + 12 d t

x \to 1 lim (- x^{2} - 5 x + 6)

f (x) = e^{x} cos (2 x)

What is the limit as x approaches 8+of 1/(x-8)-1/(sqrt(x-8)) ?
The limit as x approaches 8+of 1/(x-8)-1/(sqrt(x-8)) is infinity