What is the limit as x approaches 7+of (x-8)/(x-7) ?

The limit as x approaches 7+of (x-8)/(x-7) is -infinity

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limit as x approaches 7+of (x-8)/(x-7)

x \to 7 + lim (\frac{x - 8}{x - 7})

- \infty

Solution steps

x \to 7 + lim (\frac{x - 8}{x - 7})

\frac{x - 8}{x - 7} = (x - 8) \frac{1}{x - 7}

= x \to 7 + lim ((x - 8) \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 (x - 8) \cdot x \to 7 + lim (\frac{1}{x - 7})

x \to 7 + lim (x - 8) = - 1

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

= (- 1) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

x \to 6 lim (- x^{2} + 6 x)

x \to 3 lim (3 - 7 x - 5 x^{2})

x \to 0 lim (ln (3))

x \to 0 lim (\frac{10 x}{x ^{2} + 1})

x \to 1 lim (\frac{2 - 2}{x - 1})

What is the limit as x approaches 7+of (x-8)/(x-7) ?
The limit as x approaches 7+of (x-8)/(x-7) is -infinity