What is the limit as x approaches 5+of (7-2x)/(x-5) ?

The limit as x approaches 5+of (7-2x)/(x-5) is -infinity

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limit as x approaches 5+of (7-2x)/(x-5)

x \to 5 + lim (\frac{7 - 2 x}{x - 5})

- \infty

Solution steps

x \to 5 + lim (\frac{7 - 2 x}{x - 5})

\frac{7 - 2 x}{x - 5} = (7 - 2 x) \frac{1}{x - 5}

= x \to 5 + lim ((7 - 2 x) \frac{1}{x - 5})

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 5 + lim (7 - 2 x) \cdot x \to 5 + lim (\frac{1}{x - 5})

x \to 5 + lim (7 - 2 x) = - 3

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

= (- 3) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

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

x \to 0 lim (\frac{5 x + 3}{2 x ^{2}})

x \to 3 + lim (\frac{2 - x}{x - 3})

x \to 1 lim (\frac{3}{( x - 1 ) ^{6}})

x \to - 2 - lim (x^{2} - 4)

What is the limit as x approaches 5+of (7-2x)/(x-5) ?
The limit as x approaches 5+of (7-2x)/(x-5) is -infinity