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

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

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

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

\infty

Solution steps

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

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

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

Divide by highest denominator power:

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

= 5 \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

= 5 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

f (x) = \frac{6}{3 x + 1}, at x = - 1

y = \frac{0.9 e ^{x}}{tan ( x )}

f (x) = - 4 sin (2 x) + 3 cos (3 x)

\int \frac{x ^{3} - 4 x ^{2} - 4 x + 20}{x ^{2} - 5} d x

f (x) = 8 e^{- x} + e^{3 x}

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