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 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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