What is the limit as x approaches 3+of (7x-5)/(x-3) ?

The limit as x approaches 3+of (7x-5)/(x-3) is infinity

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limit as x approaches 3+of (7x-5)/(x-3)

x \to 3 + lim (\frac{7 x - 5}{x - 3})

\infty

Solution steps

x \to 3 + lim (\frac{7 x - 5}{x - 3})

\frac{7 x - 5}{x - 3} = (7 x - 5) \frac{1}{x - 3}

= x \to 3 + lim ((7 x - 5) \frac{1}{x - 3})

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

With the exception of indeterminate form

= x \to 3 + lim (7 x - 5) \cdot x \to 3 + lim (\frac{1}{x - 3})

x \to 3 + lim (7 x - 5) = 16

x \to 3 + lim (\frac{1}{x - 3}) = \infty

= 16 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 4 lim (\frac{3 x - 1}{x - 4})

x \to 2 lim (3 x^{2} + 5)

x \to \frac{2 π}{3} lim (sin (x))

x \to 0 + lim ((e^{x} + 10)^{5 x})

x \to 4 lim (2 x + 5)

What is the limit as x approaches 3+of (7x-5)/(x-3) ?
The limit as x approaches 3+of (7x-5)/(x-3) is infinity