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

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

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

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

- \infty

Solution steps

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

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

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

Divide by highest denominator power:

\frac{1}{1 + \frac{1}{x}}

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

For

x

approaching

- 1

from the right

, x > - 1 \Rightarrow 1 + \frac{1}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= 2 (- \infty)

Apply Infinity Property:

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

= - \infty

\frac{d}{d x} (x^{2}, x)

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

\int sin (5 π t) d t

\frac{d}{d x} (3 x + \frac{5}{x})

\frac{d y}{d x} = \frac{10 x}{7 y}

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