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 left

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

The denominator is a positive quantity approaching 0 from the right

= - \infty

x \to 0 lim (tan (x) csc (x))

x \to 4 + lim (4 - x)

x \to 4 lim (x - 2)

x \to 0 lim (\frac{f ( x )}{x ^{6}})

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

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