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

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

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

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

- \infty

Solution steps

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

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

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

For

x

approaching

2

from the right

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

The denominator is a positive quantity approaching 0 from the right

= - \infty

x \to 3 lim (x^{3} + 5 x^{2} - 8)

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

t \to 0 lim (csc (t) - cot (t))

x \to - 10 lim (\frac{x ^{2} + 25}{x})

x \to 0 lim (- \frac{sin ( x )}{x})

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