What is the limit as x approaches 1 of (2x-2)/(\sqrt[3]{26+x)-3} ?

The limit as x approaches 1 of (2x-2)/(\sqrt[3]{26+x)-3} is 54

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limit as x approaches 1 of (2x-2)/(\sqrt[3]{26+x)-3}

x \to 1 lim (\frac{2 x - 2}{3 26 + x - 3})

54

Solution steps

x \to 1 lim (\frac{2 x - 2}{3 26 + x - 3})

Apply L'Hopital's Rule

: x \to 1 lim \frac{2}{\frac{1}{3 ( x + 26 ) ^{\frac{2}{3}}}}

= x \to 1 lim \frac{2}{\frac{1}{3 ( x + 26 ) ^{\frac{2}{3}}}}

Plug in the value

x = 1

= \frac{2}{\frac{1}{3 ( 1 + 26 ) ^{\frac{2}{3}}}}

Simplify

\frac{2}{\frac{1}{3 ( 1 + 26 ) ^{\frac{2}{3}}}} : 54

= 54

x \to 3 lim (\frac{12 - x}{x + 3})

x \to \frac{π}{2} + lim (tan (π - x))

x \to 3 lim (2 x - 2)

x \to 5 lim (3 x + 5)

x \to \infty lim (\frac{2 x}{2 ^{x} ln ( 2 )})

What is the limit as x approaches 1 of (2x-2)/(\sqrt[3]{26+x)-3} ?
The limit as x approaches 1 of (2x-2)/(\sqrt[3]{26+x)-3} is 54