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

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

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

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

\infty

Solution steps

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

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

x \to 2 - lim (2) = 2

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

= 2 - (- \infty)

Simplify

2 - (- \infty) : \infty

= \infty

\frac{d y}{d x} = \frac{4 x ^{2} + 2 x}{y ^{2}}

f (x) = \frac{1}{x ^{2}}, 1, at x = 1

x \to 7 lim (\frac{x ^{7}}{700})

n = 0 \sum \infty 4 (\frac{3}{5})^{n}

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

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