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

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

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

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

- \infty

Solution steps

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

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

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

x \to 4 + lim (3 + x) = 7

x \to 4 + lim (\frac{1}{4 - x}) = - \infty

= 7 (- \infty)

Apply Infinity Property:

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

= - \infty

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