What is the limit as x approaches 7+of (x-10)/(x-7) ?

The limit as x approaches 7+of (x-10)/(x-7) is -infinity

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limit as x approaches 7+of (x-10)/(x-7)

x \to 7 + lim (\frac{x - 10}{x - 7})

- \infty

Solution steps

x \to 7 + lim (\frac{x - 10}{x - 7})

\frac{x - 10}{x - 7} = (x - 10) \frac{1}{x - 7}

= x \to 7 + lim ((x - 10) \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 - 10) \cdot x \to 7 + lim (\frac{1}{x - 7})

x \to 7 + lim (x - 10) = - 3

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

= (- 3) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

What is the limit as x approaches 7+of (x-10)/(x-7) ?
The limit as x approaches 7+of (x-10)/(x-7) is -infinity