What is the limit as x approaches 2+of (3+x)/(6-3x) ?

The limit as x approaches 2+of (3+x)/(6-3x) is -infinity

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limit as x approaches 2+of (3+x)/(6-3x)

x \to 2 + lim (\frac{3 + x}{6 - 3 x})

- \infty

Solution steps

x \to 2 + lim (\frac{3 + x}{6 - 3 x})

\frac{3 + x}{6 - 3 x} = (3 + x) \frac{1}{6 - 3 x}

= x \to 2 + lim ((3 + x) \frac{1}{6 - 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 2 + lim (3 + x) \cdot x \to 2 + lim (\frac{1}{6 - 3 x})

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

x \to 2 + lim (\frac{1}{6 - 3 x}) = - \infty

= 5 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 0 lim (x^{2} + x - \frac{1}{x} - 1)

x \to 0 lim (\frac{- 4}{x ^{2}})

x \to 0 + lim (\frac{1}{x} - \frac{1}{x ^{3} - x})

x \to 2 lim (4 x^{2} - 2 x + 1)

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

What is the limit as x approaches 2+of (3+x)/(6-3x) ?
The limit as x approaches 2+of (3+x)/(6-3x) is -infinity