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

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

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

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

\infty

Solution steps

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

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

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

Divide by highest denominator power:

\frac{1}{1 - \frac{3}{x}}

= 3 \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 positive quantity approaching 0 from the right

= 3 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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

f (x) = \frac{x ^{2}}{x - 3}, at x = 0

\frac{\partial}{\partial x} (cos (x + 9 y))

y d y = x d x

\frac{d}{d y} (9 - y^{2})

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