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

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

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limit as x approaches 3+of (e^x)/(x-3)

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

\infty

Solution steps

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

\frac{e ^{x}}{x - 3} = e^{x} \frac{1}{x - 3}

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

x \to 3 + lim (e^{x}) = e^{3}

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

= e^{3} \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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

x \to 0 lim (- (2^{\frac{1}{x}}))

x \to 3 lim (\frac{4 - x ^{2}}{x + 3})

x \to 6 lim (\frac{x ^{2} - 4}{x - 6})

h \to 0 lim (\frac{( h - 2 ) ^{3} + 8}{h})

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