What is the limit as x approaches 5-of 2/(x-5)+1 ?

The limit as x approaches 5-of 2/(x-5)+1 is -infinity

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limit as x approaches 5-of 2/(x-5)+1

x \to 5 - lim (\frac{2}{x - 5} + 1)

- \infty

Solution steps

x \to 5 - lim (\frac{2}{x - 5} + 1)

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

With the exception of indeterminate form

= x \to 5 - lim (\frac{2}{x - 5}) + x \to 5 - lim (1)

x \to 5 - lim (\frac{2}{x - 5}) = - \infty

x \to 5 - lim (1) = 1

= - \infty + 1

Apply Infinity Property:

- \infty + c = - \infty

= - \infty

What is the limit as x approaches 5-of 2/(x-5)+1 ?
The limit as x approaches 5-of 2/(x-5)+1 is -infinity