What is the limit as x approaches 7-of (4-3x)/(x-7) ?

The limit as x approaches 7-of (4-3x)/(x-7) is infinity

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limit as x approaches 7-of (4-3x)/(x-7)

x \to 7 - lim (\frac{4 - 3 x}{x - 7})

\infty

Solution steps

x \to 7 - lim (\frac{4 - 3 x}{x - 7})

\frac{4 - 3 x}{x - 7} = (4 - 3 x) \frac{1}{x - 7}

= x \to 7 - lim ((4 - 3 x) \frac{1}{x - 7})

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 7 - lim (4 - 3 x) \cdot x \to 7 - lim (\frac{1}{x - 7})

x \to 7 - lim (4 - 3 x) = - 17

x \to 7 - lim (\frac{1}{x - 7}) = - \infty

= (- 17) (- \infty)

Apply Infinity Property:

- c \cdot (- \infty) = \infty

= \infty

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What is the limit as x approaches 7-of (4-3x)/(x-7) ?
The limit as x approaches 7-of (4-3x)/(x-7) is infinity