What is the limit as x approaches-3-of (2x)/(x+3) ?

The limit as x approaches-3-of (2x)/(x+3) is infinity

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limit as x approaches-3-of (2x)/(x+3)

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

\infty

Solution steps

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

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

= 2 \cdot x \to - 3 - lim (\frac{x}{x + 3})

Divide by highest denominator power:

\frac{1}{1 + \frac{3}{x}}

= 2 \cdot x \to - 3 - lim (\frac{1}{1 + \frac{3}{x}})

For

x

approaching

- 3

from the left

, x < - 3 \Rightarrow 1 + \frac{3}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= 2 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

y = sin^{2} (x), y = sin^{3} (x), [0, π]

n = 0 \sum \infty (x + 1)^{n}

\frac{d}{d x} (2 x y^{4} - 3)

\frac{\partial}{\partial x} (2 x^{3} y + sin (x^{3}))

What is the limit as x approaches-3-of (2x)/(x+3) ?
The limit as x approaches-3-of (2x)/(x+3) is infinity