Lim x- 1 1- x 1-3 - 1- x 1-5 is equal to

The correct option is A 1 Given, lim _x→ 1(1+x^1/31+x^1/5) substitute x=1 =1+1^1/31+1^1/5 =1 ...

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Standard XII

Mathematics

Substitution Method to Remove Indeterminate Form

lim x→ 1 1+ x...

Question

$lim x \to 1 \frac{1 + x^{1 / 3}}{1 + x^{1 / 5}}$ is equal to

1

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- 1

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0.5

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Solution

The correct option is A $1$
Given,

${lim}_{x \to 1} ⎛ ⎝ \frac{1 + x^{\frac{1}{3}}}{1 + x^{\frac{1}{5}}} ⎞ ⎠$

substitute $x = 1$

$= \frac{1 + 1^{\frac{1}{3}}}{1 + 1^{\frac{1}{5}}}$

$= 1$

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{lim}_{x \to 1} \frac{1 - x^{1 / 3}}{1 - x^{1 / 4}} =

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Q. The value of

lim x \to 0 \frac{(1 + x)^{\frac{1}{2}} - 1}{(1 + x)^{\frac{1}{2}} - 1}

is equal to

lim x \to 0 \frac{2^{x} - 1}{{(1 + x)}^{1 / 2} - 1}

is equal to

$l i m x \to - 1 \frac{(1 + x) (1 - x^{2}) (1 + x^{3}) (1 - x^{4}) . . . . (1 - x^{4 n})}{{[(1 + x) (1 - x^{2}) (1 + x^{3}) (1 + x^{4}) . . . . . . . (1 - x^{2 n})]}^{2}} is equal to:$

{lim}_{x \to 0} \frac{(1 + x)^{1 / 4} - (1 - x)^{1 / 4}}{x}

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limx→11+x1/31+x1/5 is equal to

The correct option is A 1Given,limx→1⎛⎝1+x131+x15⎞⎠substitute x=1=1+1131+115=1

$lim x \to 1 \frac{1 + x^{1 / 3}}{1 + x^{1 / 5}}$ is equal to

The correct option is A $1$
Given,

${lim}_{x \to 1} ⎛ ⎝ \frac{1 + x^{\frac{1}{3}}}{1 + x^{\frac{1}{5}}} ⎞ ⎠$

substitute $x = 1$

$= \frac{1 + 1^{\frac{1}{3}}}{1 + 1^{\frac{1}{5}}}$

$= 1$