What is the limit as x approaches 3+of (4x)/(x-3) ?

The limit as x approaches 3+of (4x)/(x-3) is infinity

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limit as x approaches 3+of (4x)/(x-3)

x \to 3 + lim (\frac{4 x}{x - 3})

\infty

Solution steps

x \to 3 + lim (\frac{4 x}{x - 3})

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

= 4 \cdot x \to 3 + lim (\frac{x}{x - 3})

Divide by highest denominator power:

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

= 4 \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

= 4 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

y = 8 (x - \frac{1}{x})^{4}, at x = 2

\frac{( x ^{2} - 1 )}{x - 1}

x \to 0 lim (\frac{6 e ^{x} - 6}{x})

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

\frac{d}{d x} (cos (4 x) + sin (4 x))

What is the limit as x approaches 3+of (4x)/(x-3) ?
The limit as x approaches 3+of (4x)/(x-3) is infinity