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

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

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

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

- \infty

Solution steps

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

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

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

For

x

approaching

1

from the right

, x > 1 \Rightarrow x - 1 > 0

The denominator is a positive quantity approaching 0 from the right

= - \infty

x \to 0 lim (\frac{5 x + 3}{2 x ^{2}})

x \to 3 + lim (\frac{2 - x}{x - 3})

x \to 1 lim (\frac{3}{( x - 1 ) ^{6}})

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

x \to 0 - lim (3 x + 2)

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