What is the limit as x approaches 5+of-x/(x-5) ?

The limit as x approaches 5+of-x/(x-5) is -infinity

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limit as x approaches 5+of-x/(x-5)

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

- \infty

Solution steps

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

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

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

Divide by highest denominator power:

\frac{1}{1 - \frac{5}{x}}

= - x \to 5 + lim (\frac{1}{1 - \frac{5}{x}})

For

x

approaching

5

from the right

, x > 5 \Rightarrow 1 - \frac{5}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= - \infty

\int \frac{1}{y ^{2} - 2 y} d y

3 y^{^{'}} + y = 0, y (0) = 0

n \to \infty lim (\frac{1}{e})

\int \frac{5 ( x ^{2} + 4 )}{x ( x ^{2} + 5 )} d x

x \to 0 lim (+ (sin (x)))

What is the limit as x approaches 5+of-x/(x-5) ?
The limit as x approaches 5+of-x/(x-5) is -infinity