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

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

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

x \to + 3 lim ((\frac{x - 1}{2 x - 4})^{\frac{1}{x - 3}})

\frac{1}{e}

Decimal

0.60653 \dots

Solution steps

x \to 3 lim ((\frac{x - 1}{2 x - 4})^{\frac{1}{x - 3}})

Apply exponent rules

= x \to 3 lim (e^{\frac{1}{x - 3} l n (\frac{x - 1}{2 x - 4})})

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

y^{^{''}} = - 4 \cdot y

\int \frac{1}{16 e ^{- 3 x} + e ^{3 x}} d x

y = x e^{x}

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 4)^{7})

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

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