What is the limit as x approaches 1-of-1/((x-1)^2) ?

The limit as x approaches 1-of-1/((x-1)^2) is -infinity

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limit as x approaches 1-of-1/((x-1)^2)

x \to 1 - lim (- \frac{1}{( x - 1 ) ^{2}})

- \infty

Solution steps

x \to 1 - lim (- \frac{1}{( x - 1 ) ^{2}})

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

= - x \to 1 - lim (\frac{1}{( x - 1 ) ^{2}})

For

x

approaching

1

from the left

, x < 1 \Rightarrow (x - 1)^{2} > 0

The denominator is a positive quantity approaching 0 from the right

= - \infty

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

x \to 3 + lim (\frac{x}{9 - x ^{2}})

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

x \to - 6 + lim (x + 6 + x)

x \to 3 - lim (\frac{\frac{1}{x}}{2 x})

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