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) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

9 x^{\frac{1}{2}}

f (x) = x + \frac{1}{x}, at x = 4

\frac{d}{d x} (7 x^{6})

x \to 0 lim (\frac{( sin ( 3 x ) )}{x})

x^{2} y^{^{''}} - 5 x y^{^{'}} + 9 y = 0

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