What is the limit as x approaches 3+of (e^2x)/(x-3) ?

The limit as x approaches 3+of (e^2x)/(x-3) is infinity

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limit as x approaches 3+of (e^2x)/(x-3)

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

\infty

Solution steps

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

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

= e^{2} \cdot x \to 3 + lim (\frac{x}{x - 3})

Divide by highest denominator power:

\frac{1}{1 - \frac{3}{x}}

= e^{2} \cdot x \to 3 + lim (\frac{1}{1 - \frac{3}{x}})

For

x

approaching

3

from the right

, x > 3 \Rightarrow 1 - \frac{3}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= e^{2} \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\int \frac{1}{x ^{2} + 6 x} d x

\int (x + 1) d x

\frac{d}{d z} (9 z^{2} e^{z})

(2, - 3), (4, 4)

\frac{\partial}{\partial x} (z y^{3})

What is the limit as x approaches 3+of (e^2x)/(x-3) ?
The limit as x approaches 3+of (e^2x)/(x-3) is infinity