What is the limit as x approaches 4+of ((7x))/(x-4) ?

The limit as x approaches 4+of ((7x))/(x-4) is infinity

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limit as x approaches 4+of ((7x))/(x-4)

x \to 4 + lim (\frac{( 7 x )}{x - 4})

\infty

Solution steps

x \to 4 + lim (\frac{7 x}{x - 4})

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

= 7 \cdot x \to 4 + lim (\frac{x}{x - 4})

Divide by highest denominator power:

\frac{1}{1 - \frac{4}{x}}

= 7 \cdot x \to 4 + lim (\frac{1}{1 - \frac{4}{x}})

For

x

approaching

4

from the right

, x > 4 \Rightarrow 1 - \frac{4}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= 7 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\int \frac{8}{4 x ^{2} + 1} d x

y = 1 - x^{2}, y = 29 - 11 x

2 (3 x - 8)^{4} - 5 x + 6

x \to 1 + lim (cos (π x))

x \to 3 lim (\frac{x}{x ^{2} + 1})

What is the limit as x approaches 4+of ((7x))/(x-4) ?
The limit as x approaches 4+of ((7x))/(x-4) is infinity