What is the limit as x approaches 2 of ((x+3)/(2x+1))^{2/(x-2)} ?

The limit as x approaches 2 of ((x+3)/(2x+1))^{2/(x-2)} is 1/(e^{2/5)}

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limit as x approaches 2 of ((x+3)/(2x+1))^{2/(x-2)}

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

\frac{1}{e ^{\frac{2}{5}}}

Decimal Notation

0.67032 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e ^{\frac{2}{5}}}

= \frac{1}{e ^{\frac{2}{5}}}

\frac{d}{d x} (x arccos (3 x))

\int_{- 2}^{4} \frac{1}{( x - 3 ) ^{3}} d x

\frac{d y}{d x}, y = 2 x^{3}

\int e^{3 x} sin (4 x) d x

f (x) = \frac{3}{x ^{2}} - \frac{1}{x}

What is the limit as x approaches 2 of ((x+3)/(2x+1))^{2/(x-2)} ?
The limit as x approaches 2 of ((x+3)/(2x+1))^{2/(x-2)} is 1/(e^{2/5)}