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

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

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

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

- \infty

Solution steps

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

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

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

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

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

= 2 (- \infty)

Apply Infinity Property:

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

= - \infty

\int 15 tan^{2} (x) sec^{3} (x) d x

2 x e^{4 x}

\frac{d}{d θ} (4 sin (2 θ))

\int \frac{2}{x ^{3} x ^{2} - 3} d x

2 x + 3 x

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