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

The limit as x approaches 2 of (((3x+2))/(5x-2))^{((3))/(x-2)} is 1/(e^{3/4)}

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

x \to 2 lim (\frac{( 3 x + 2 )}{5 x - 2})^{\frac{( 3 )}{x - 2}}

\frac{1}{e ^{\frac{3}{4}}}

Decimal

0.47236 \dots

Solution steps

x \to 2 lim ((\frac{3 x + 2}{5 x - 2})^{\frac{3}{x - 2}})

Apply exponent rules

= x \to 2 lim (e^{\frac{3}{x - 2} l n (\frac{3 x + 2}{5 x - 2})})

Apply the Limit Chain Rule:

\frac{1}{e ^{\frac{3}{4}}}

= \frac{1}{e ^{\frac{3}{4}}}

x \to \infty lim (x^{6} e^{- x^{5}})

\int sinh (1 + 4 x) d x

l a pl a ce t r an s f or m (t^{2} + \frac{1}{2})^{2}

(x^{2} + 2 y^{2}) d x - x y d y = 0

t an g e n t y = 2 sin (x), at x = \frac{3}{4} π

What is the limit as x approaches 2 of (((3x+2))/(5x-2))^{((3))/(x-2)} ?
The limit as x approaches 2 of (((3x+2))/(5x-2))^{((3))/(x-2)} is 1/(e^{3/4)}