What is the limit as x approaches 1/5+of x/(10x-2) ?

The limit as x approaches 1/5+of x/(10x-2) is infinity

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limit as x approaches 1/5+of x/(10x-2)

x \to \frac{1}{5} + lim (\frac{x}{10 x - 2})

\infty

Solution steps

x \to \frac{1}{5} + lim (\frac{x}{10 x - 2})

Divide by highest denominator power:

\frac{1}{10 - \frac{2}{x}}

= x \to \frac{1}{5} + lim (\frac{1}{10 - \frac{2}{x}})

For

x

approaching

\frac{1}{5}

from the right

, x > \frac{1}{5} \Rightarrow 10 - \frac{2}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

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What is the limit as x approaches 1/5+of x/(10x-2) ?
The limit as x approaches 1/5+of x/(10x-2) is infinity