What is the limit as x approaches 0+of (e^{4x})/(3x) ?

The limit as x approaches 0+of (e^{4x})/(3x) is infinity

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limit as x approaches 0+of (e^{4x})/(3x)

x \to 0 + lim (\frac{e ^{4 x}}{3 x})

\infty

Solution steps

x \to 0 + lim (\frac{e ^{4 x}}{3 x})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{3} \cdot x \to 0 + lim (\frac{e ^{4 x}}{x})

\frac{e ^{4 x}}{x} = e^{4 x} \frac{1}{x}

= \frac{1}{3} \cdot x \to 0 + lim (e^{4 x} \frac{1}{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

= \frac{1}{3} \cdot x \to 0 + lim (e^{4 x}) \cdot x \to 0 + lim (\frac{1}{x})

x \to 0 + lim (e^{4 x}) = 1

x \to 0 + lim (\frac{1}{x}) = \infty

= \frac{1}{3} \cdot 1 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

x \to 1 - lim (\frac{x ^{3}}{x ^{2} - 1})

(0, 0), (9, \frac{9}{7})

\int \frac{x ^{3} + x + 1}{x ^{4} + 2 x ^{2} + 1} d x

160 + 3.2 x - 0.03 x^{2}

\frac{d}{d x} (9 x sin (π x))

What is the limit as x approaches 0+of (e^{4x})/(3x) ?
The limit as x approaches 0+of (e^{4x})/(3x) is infinity