What is the limit as x approaches 1 of (2-x)/(x^2-4) ?

The limit as x approaches 1 of (2-x)/(x^2-4) is -1/3

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limit as x approaches 1 of (2-x)/(x^2-4)

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

- \frac{1}{3}

Decimal

- 0.33333 \dots

Solution steps

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

Plug in the value

x = 1

= \frac{2 - 1}{1 ^{2} - 4}

Simplify

= - \frac{1}{3}

x \to 0 lim (\frac{1}{x ^{- 2}})

x \to 3 lim (x - 3 x + 1 - 2)

x \to 0 lim (cos (2 x - 1))

x \to 0 lim ((2^{x} + x)^{\frac{3}{x}})

x \to 1 lim (ln (x) + 1)

What is the limit as x approaches 1 of (2-x)/(x^2-4) ?
The limit as x approaches 1 of (2-x)/(x^2-4) is -1/3