What is the limit as x approaches 2+of (3x+1)/(2-x) ?

The limit as x approaches 2+of (3x+1)/(2-x) is -infinity

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limit as x approaches 2+of (3x+1)/(2-x)

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

- \infty

Solution steps

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

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

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

x \to 2 + lim (3 x + 1) = 7

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

= 7 (- \infty)

Apply Infinity Property:

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

= - \infty

x \to 0 lim ((1 - cos (x))^{x})

x \to 1 lim (x - 4)

x \to 0 lim (ln (ln (x)))

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

x \to 2 lim (6 x^{2} + 7 x - 3)

What is the limit as x approaches 2+of (3x+1)/(2-x) ?
The limit as x approaches 2+of (3x+1)/(2-x) is -infinity