What is the limit as x approaches-5-of (3x)/(2x+10) ?

The limit as x approaches-5-of (3x)/(2x+10) is infinity

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limit as x approaches-5-of (3x)/(2x+10)

x \to - 5 - lim (\frac{3 x}{2 x + 10})

\infty

Solution steps

x \to - 5 - lim (\frac{3 x}{2 x + 10})

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

= 3 \cdot x \to - 5 - lim (\frac{x}{2 x + 10})

Divide by highest denominator power:

\frac{1}{2 + \frac{10}{x}}

= 3 \cdot x \to - 5 - lim (\frac{1}{2 + \frac{10}{x}})

For

x

approaching

- 5

from the left

, x < - 5 \Rightarrow 2 + \frac{10}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= 3 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 0 - lim ((\frac{1}{5})^{\frac{1}{x}})

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

x \to \infty + lim (x ln (x))

f (x) = x^{3} - 7 x^{2} + 6 x + 1

\int e^{x^{3}} x d x

What is the limit as x approaches-5-of (3x)/(2x+10) ?
The limit as x approaches-5-of (3x)/(2x+10) is infinity