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

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

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

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

\infty

Solution steps

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

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

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

x \to 3 - lim (1 - 2 x) = - 5

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

= (- 5) (- \infty)

Apply Infinity Property:

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

= \infty

\frac{d}{d x} (sin^{2} (2 b x))

\int \frac{6 + x + x ^{2}}{x} d x

\frac{d x}{d t} = - 3 x + 6 e^{- t}

\frac{d}{d x} (x^{3} - 4 x^{2} + 45 x + 10)

\int_{0}^{5} x e^{- 2 x} d x

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