What is the limit as x approaches 3-of (4-x)/(x-3) ?

The limit as x approaches 3-of (4-x)/(x-3) is -infinity

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limit as x approaches 3-of (4-x)/(x-3)

x \to 3 - lim (\frac{4 - x}{x - 3})

- \infty

Solution steps

x \to 3 - lim (\frac{4 - x}{x - 3})

\frac{4 - x}{x - 3} = (4 - x) \frac{1}{x - 3}

= x \to 3 - lim ((4 - 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 (4 - x) \cdot x \to 3 - lim (\frac{1}{x - 3})

x \to 3 - lim (4 - x) = 1

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

= 1 \cdot (- \infty)

Apply Infinity Property:

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

= - \infty

\int_{0}^{10} 1 + x d x

\int_{- \infty}^{0} \frac{1}{6 - 5 x} d x

24 x (3 x^{2} - 1)^{3}

x^{2} \cdot \frac{d y}{d x} = y - x y

\int (x^{2} y) d y

What is the limit as x approaches 3-of (4-x)/(x-3) ?
The limit as x approaches 3-of (4-x)/(x-3) is -infinity