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

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

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

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

\infty

Solution steps

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

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

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

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

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

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

= (- 2) (- \infty)

Apply Infinity Property:

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

= \infty

\int y (2 y + 1) e^{4 y^{3} + 3 y^{2} - 4} d y

5 x^{2} - x^{3}

\int (5 - \frac{2}{3} x^{2} + \frac{3}{4} x^{3}) d x

x \frac{d y}{d x} + 2 y = 5 x^{3}

\int \frac{39}{39 + e ^{x}} d x

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