What is the limit as x approaches 3+of (3x-10)/(3-x) ?

The limit as x approaches 3+of (3x-10)/(3-x) is infinity

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limit as x approaches 3+of (3x-10)/(3-x)

x \to 3 + lim (\frac{3 x - 10}{3 - x})

\infty

Solution steps

x \to 3 + lim (\frac{3 x - 10}{3 - x})

\frac{3 x - 10}{3 - x} = (3 x - 10) \frac{1}{3 - x}

= x \to 3 + lim ((3 x - 10) \frac{1}{3 - x})

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 (3 x - 10) \cdot x \to 3 + lim (\frac{1}{3 - x})

x \to 3 + lim (3 x - 10) = - 1

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

= (- 1) (- \infty)

Apply Infinity Property:

- c \cdot (- \infty) = \infty

= \infty

x \to 2 lim (2 + ∣ 2 x - 4 ∣)

x \to - \infty lim (- 7 x - 1)

x \to 1 lim (\frac{x - ∣ x ∣}{2 x})

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

x \to - 0.75 lim (x^{2} + 3)

What is the limit as x approaches 3+of (3x-10)/(3-x) ?
The limit as x approaches 3+of (3x-10)/(3-x) is infinity