Evaluate- - lim-x- 1x-2-3-1x-3-4-1- 5-9- 9-5- 8-9- 0-

The correct option is C 8/9 Given: #160; lim_x→ 1x^ 2/3 1x^ 3/4 1 =lim _ x→ 1 2 / 3 x^ 5 / 3 #160; 3 / 4 x^ 7 / 4 #160; ....... ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Limits

Evaluate: ...

Question

Evaluate: $lim x \to 1 \frac{x^{\frac{- 2}{3}} - 1}{x^{\frac{- 3}{4}} - 1}$

\frac{5}{9}

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\frac{9}{5}

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\frac{8}{9}

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Solution

The correct option is C $\frac{8}{9}$
Given: $lim x \to 1 \frac{x^{\frac{- 2}{3}} - 1}{x^{\frac{- 3}{4}} - 1}$

$= {lim}_{x \to 1} \frac{\frac{- 2}{3} x^{\frac{- 5}{3}}}{\frac{- 3}{4} x^{\frac{- 7}{4}}}$ ....... $(U s i n g \frac{d}{d x} x^{n} = n x^{n - 1})$

$= \frac{8}{9} lim x \to 1 x^{\frac{1}{12}}$
$= \frac{8}{9}$

Hence, option $^{'} C^{'}$ is correct.

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Similar questions

Evaluate : $(i) \frac{5}{9} + \frac{- 7}{6} (i i) 4 + \frac{3}{- 5} (i i i) \frac{1}{- 15} + \frac{5}{- 12} (i v) \frac{5}{9} + \frac{3}{- 4} (v) \frac{- 8}{9} + \frac{- 5}{12} (v i) 0 + \frac{- 2}{7} (v i i) \frac{5}{- 11} + 0 (v i i i) 2 + \frac{- 3}{5} (i x) \frac{4}{- 9} + 1$

Q. Evaluate:

(i) \frac{3}{7} + \frac{- 4}{9} - \frac{- 11}{7} - \frac{7}{9}

(i i) \frac{2}{3} + \frac{- 4}{5} - \frac{1}{3} - \frac{2}{5}

(i i i) \frac{4}{7} - \frac{- 8}{9} - \frac{- 13}{7} + \frac{17}{9}

Evaluate :

$(i) \frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5} (i i i) \frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{9} (i v) \frac{3}{8} + \frac{- 5}{12} + \frac{3}{7} + \frac{3}{12} + \frac{- 5}{8} + \frac{- 2}{7}$