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

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

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

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

- \infty

Solution steps

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

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

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

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

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

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

= (- 3) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

cos (x^{2}) \cdot 2 x

16

\frac{d}{d x} (e^{t a n (x^{3})})

\int \frac{2 e ^{2 x}}{e ^{2 x} + 10 e ^{x} + 24} d x

- \frac{5}{x ^{2}}

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