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}})

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

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