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Maths-

General

Easy

Question

$n rightwards arrow infinity vertical line i m left square bracket fraction numerator 1 over denominator n to the power of 3 end exponent plus 1 end fraction plus fraction numerator 4 over denominator n to the power of 3 end exponent plus 1 end fraction plus fraction numerator 9 over denominator n to the power of 3 end exponent plus 1 end fraction plus midline horizontal ellipsis plus fraction numerator n to the power of 2 end exponent over denominator n to the power of 3 end exponent plus 1 end fraction right square bracket equals$

1
$\frac{2}{3}$
$\frac{1}{3}$
$0$

The correct answer is: $1 third$

Related Questions to study

The value of $n rightwards arrow infinity vertical line i m fraction numerator chi to the power of n end exponent over denominator x to the power of n end exponent plus 1 end fraction$ where $chi less than negative 1$ is

The value of $n rightwards arrow infinity vertical line i m fraction numerator chi to the power of n end exponent over denominator x to the power of n end exponent plus 1 end fraction$ where $chi less than negative 1$ is

$S plus fraction numerator 3 over denominator 2 end fraction O subscript 2 end subscript ⟶ S O subscript 3 end subscript plus 2 x k c a l$
$S O subscript 2 end subscript plus fraction numerator 1 over denominator 2 end fraction O subscript 2 end subscript ⟶ S O subscript 3 end subscript plus y k c a l$
The heat of formation of S0₂ is:

$S plus fraction numerator 3 over denominator 2 end fraction O subscript 2 end subscript ⟶ S O subscript 3 end subscript plus 2 x k c a l$
$S O subscript 2 end subscript plus fraction numerator 1 over denominator 2 end fraction O subscript 2 end subscript ⟶ S O subscript 3 end subscript plus y k c a l$
The heat of formation of S0₂ is:

Chemistry-General

One mole of an ideal gas at 300 K is expanded isothermally from an initial volume of 1 litre to 10 litre. The M for this process is: (R = 2 cal K^-1 mol^-I)

One mole of an ideal gas at 300 K is expanded isothermally from an initial volume of 1 litre to 10 litre. The M for this process is: (R = 2 cal K^-1 mol^-I)

Chemistry-General

parallel

In an electrochemical cell, if EO is the emf of the cell involving n mole of electrons, then is

In an electrochemical cell, if EO is the emf of the cell involving n mole of electrons, then is

Chemistry-General

Given that $capital delta H subscript f end subscript left parenthesis H right parenthesis$ = 218 kJ/mol, express the H-H bond energy in kcal/mol

Given that $capital delta H subscript f end subscript left parenthesis H right parenthesis$ = 218 kJ/mol, express the H-H bond energy in kcal/mol

Chemistry-General

The value of $x rightwards arrow 0 I i m fraction numerator 2 7 to the power of chi end exponent minus 9 to the power of chi end exponent minus 3 to the power of chi end exponent plus 1 over denominator square root of 5 minus square root of 4 plus blank c o s blank x end root end fraction$ is

The value of $x rightwards arrow 0 I i m fraction numerator 2 7 to the power of chi end exponent minus 9 to the power of chi end exponent minus 3 to the power of chi end exponent plus 1 over denominator square root of 5 minus square root of 4 plus blank c o s blank x end root end fraction$ is

parallel

$x rightwards arrow 0 I i m left square bracket fraction numerator e to the power of chi end exponent minus e to the power of blank s i n blank x end exponent over denominator x minus blank s i n blank x end fraction right square bracket$ is equal to

$x rightwards arrow 0 I i m left square bracket fraction numerator e to the power of chi end exponent minus e to the power of blank s i n blank x end exponent over denominator x minus blank s i n blank x end fraction right square bracket$ is equal to

$chi rightwards arrow infinity I i m left parenthesis 1 minus fraction numerator 4 over denominator x minus 1 end fraction right parenthesis to the power of 3 x minus 1 end exponent equals$

$chi rightwards arrow infinity I i m left parenthesis 1 minus fraction numerator 4 over denominator x minus 1 end fraction right parenthesis to the power of 3 x minus 1 end exponent equals$

lim $stack e to the power of chi end exponent minus e to the power of negative x end exponent with _ below$ is $x rightwards arrow 0$ $s vertical line n x$

lim $stack e to the power of chi end exponent minus e to the power of negative x end exponent with _ below$ is $x rightwards arrow 0$ $s vertical line n x$

parallel

$x rightwards arrow 0 I i m fraction numerator x blank t a n blank 2 x minus 2 x blank t a n blank x over denominator left parenthesis 1 minus blank c o s blank 2 x right parenthesis to the power of 2 end exponent end fraction$ is

$x rightwards arrow 0 I i m fraction numerator x blank t a n blank 2 x minus 2 x blank t a n blank x over denominator left parenthesis 1 minus blank c o s blank 2 x right parenthesis to the power of 2 end exponent end fraction$ is

$stack l i m with x rightwards arrow infinity below square root of fraction numerator x plus s i n invisible function application x over denominator x minus c o s invisible function application x end fraction end root equals$

$stack l i m with x rightwards arrow infinity below square root of fraction numerator x plus s i n invisible function application x over denominator x minus c o s invisible function application x end fraction end root equals$

$stack l i m with x rightwards arrow 0 below fraction numerator x times 2 to the power of x end exponent minus x over denominator 1 minus c o s invisible function application x end fraction equals$

$stack l i m with x rightwards arrow 0 below fraction numerator x times 2 to the power of x end exponent minus x over denominator 1 minus c o s invisible function application x end fraction equals$

parallel

$stack l i m with x rightwards arrow 0 below$ $fraction numerator square root of 0 plus 2 x end root minus square root of 3 x end root over denominator square root of 30 plus x end root minus 2 square root of chi end fraction equals$

$stack l i m with x rightwards arrow 0 below$ $fraction numerator square root of 0 plus 2 x end root minus square root of 3 x end root over denominator square root of 30 plus x end root minus 2 square root of chi end fraction equals$

$chi rightwards arrow right ceiling I i m fraction numerator x minus 1 over denominator 2 x to the power of 2 end exponent minus 7 x plus 5 end fraction equals$

$chi rightwards arrow right ceiling I i m fraction numerator x minus 1 over denominator 2 x to the power of 2 end exponent minus 7 x plus 5 end fraction equals$

$x rightwards arrow 0 I i m fraction numerator vertical line x vertical line over denominator chi end fraction equals$

$x rightwards arrow 0 I i m fraction numerator vertical line x vertical line over denominator chi end fraction equals$

parallel

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