What is the limit as x approaches 3+of (2x-11)/(x-3) ?

The limit as x approaches 3+of (2x-11)/(x-3) is -infinity

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limit as x approaches 3+of (2x-11)/(x-3)

x \to 3 + lim (\frac{2 x - 11}{x - 3})

- \infty

Solution steps

x \to 3 + lim (\frac{2 x - 11}{x - 3})

\frac{2 x - 11}{x - 3} = (2 x - 11) \frac{1}{x - 3}

= x \to 3 + lim ((2 x - 11) \frac{1}{x - 3})

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 3 + lim (2 x - 11) \cdot x \to 3 + lim (\frac{1}{x - 3})

x \to 3 + lim (2 x - 11) = - 5

x \to 3 + lim (\frac{1}{x - 3}) = \infty

= (- 5) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

x \to 1 lim (\frac{x ^{3} - 8}{x - 2})

x \to \frac{π}{3} lim (2 sin (5 x))

x \to 2 lim (3 x^{3} + 8 x - 4)

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

x \to 1 - lim ((1 - x) ln (1 - x))

What is the limit as x approaches 3+of (2x-11)/(x-3) ?
The limit as x approaches 3+of (2x-11)/(x-3) is -infinity