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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Plug in the value

x = 2^{2}

= \frac{1}{2 ^{2} - 2}

Simplify

= \frac{1}{2}

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

x \to - 3 lim (4 x^{2} - 3 x + 1)

x \to 3 lim (\frac{2 x - 8}{x + 4})

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

x \to 2 + lim (- \frac{16 x}{x - 2})

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