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

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

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

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

- \infty

Solution steps

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

\frac{x ^{2} + 1}{x + 2} = (x^{2} + 1) \frac{1}{x + 2}

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

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

With the exception of indeterminate form

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

x \to - 2 - lim (x^{2} + 1) = 5

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

= 5 (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

x \to - \infty lim (\frac{x}{0})

x \to 0 lim (arccot (x))

x \to 3 lim (\frac{3}{x ^{2} - 6 x + 9})

x \to 0 + lim ((g (x))^{\frac{l n ( 2 )}{x}})

x \to 1 lim (\frac{x + 1}{∣ x + 1 ∣})

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