What is the limit as x approaches 2-of 1/((x-2)^3) ?

The limit as x approaches 2-of 1/((x-2)^3) is -infinity

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limit as x approaches 2-of 1/((x-2)^3)

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

- \infty

Solution steps

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

For

x

approaching

2

from the left

, x < 2 \Rightarrow (x - 2)^{3} < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

x \to \frac{3 π}{2} lim (x sec (x))

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

x \to 7 + lim (\frac{6}{x - 7})

x \to 0 - lim (\frac{e ^{x} - 1}{x})

h \to 0 lim \frac{( 8 ( \frac{1}{2} + h ) ^{8} - 8 ( \frac{1}{2} ) ^{8} )}{h}

What is the limit as x approaches 2-of 1/((x-2)^3) ?
The limit as x approaches 2-of 1/((x-2)^3) is -infinity