What is the limit as x approaches-3+of (-7x)/(x+3) ?

The limit as x approaches-3+of (-7x)/(x+3) is infinity

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limit as x approaches-3+of (-7x)/(x+3)

x \to - 3 + lim (\frac{- 7 x}{x + 3})

\infty

Solution steps

x \to - 3 + lim (\frac{- 7 x}{x + 3})

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

= - 7 \cdot x \to - 3 + lim (\frac{x}{x + 3})

Divide by highest denominator power:

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

= - 7 \cdot x \to - 3 + lim (\frac{1}{1 + \frac{3}{x}})

For

x

approaching

- 3

from the right

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

The denominator is a negative quantity approaching 0 from the left

= - 7 (- \infty)

Apply Infinity Property:

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

= \infty

\int \frac{x}{4 - 3 x ^{2}} d x

x \to 0 lim (\frac{x + 97}{x})

x y^{^{'}} - 2 y = 2 x^{2} + 2 x + 2

g (x) = 3 e^{- 2 x}, (0, 3)

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

What is the limit as x approaches-3+of (-7x)/(x+3) ?
The limit as x approaches-3+of (-7x)/(x+3) is infinity