lim-x-1-x-1-3-1-x-1-4-1-Evaluate-this-

Question Number 25026 by NECx last updated on 02/Dec/17

\lim_{x \to 1} (\frac{x^{1 / 3} - 1}{x^{1 / 4} - 1})

E v a l u a t e t h i s

Answered by nnnavendu last updated on 02/Dec/17

\lim_{x \to 1} (\frac{x^{1 / 3} - 1}{x^{1 / 4} - 1})

\lim_{x \to 1} (\frac{{(x^{1 / 4})}^{4 / 3} - 1^{4 / 3}}{x^{1 / 4} - 1})

\lim_{x \to 1} (4 / 3 1^{\frac{4}{3} - 1})

4 / 3

f armula -

\lim_{x \to n} (\frac{x^{n} - a^{n}}{x - a}) = {n a}^{n - 1}

Commented by moxhix last updated on 02/Dec/17

I t h i n k \dots

\underset{x \to a}{l i m} (\frac{x^{n} - a^{n}}{x - a}) = {(\frac{d}{d x} x^{n})}_{x = a} = {n a}^{n - 1}

Answered by jota+ last updated on 03/Dec/17

= \frac{\lim_{x \to 1} x^{- 2 / 3} / 3}{\lim_{x \to 1} x^{- 3 / 4} / 4} = \frac{4}{3}

U s e H o p i t a l r u l e

Commented by NECx last updated on 02/Dec/17

t h a n k s b o s s e s \dots . I r e a l l y a p p r e c i a t e t h i s

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