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Maths-

General

Easy

Question

If $f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell left parenthesis 1 plus 2 x right parenthesis to the power of 1 divided by x subscript l end subscript end exponent f o r x not equal to 0 end cell row cell e subscript ´ end subscript superscript 2 end superscript f o r x equals 0 t h e n end cell end table close$

$x \to 0 + I i m f (x) = e$
$x \to 0 - I i m f (x) = e^{2}$
$f (x)$ is discontinuous at $x = 0$
None of these

The correct answer is: $x rightwards arrow 0 minus I i m f left parenthesis x right parenthesis equals e to the power of 2 end exponent$

Related Questions to study

Let $f left parenthesis x right parenthesis equals left curly bracket subscript negative x to the power of 2 end exponent minus k end subscript superscript X to the power of 2 end exponent plus k end superscript comma$ when x $greater or equal than 0$ when x $less than 0$ lf the function f(x) be continuous at x=0, then k=

Let $f left parenthesis x right parenthesis equals left curly bracket subscript negative x to the power of 2 end exponent minus k end subscript superscript X to the power of 2 end exponent plus k end superscript comma$ when x $greater or equal than 0$ when x $less than 0$ lf the function f(x) be continuous at x=0, then k=

If the function $f left parenthesis x right parenthesis equals left curly bracket subscript 3 comma w h e n x equals fraction numerator pi over denominator 2 end fraction end subscript superscript fraction numerator k blank c o s blank x over denominator pi minus 2 x end fraction w h e n x not equal to fraction numerator pi over denominator 2 end fraction end superscript$ ’ be continuous at $chi equals fraction numerator pi over denominator 2 end fraction$ , then k=

If the function $f left parenthesis x right parenthesis equals left curly bracket subscript 3 comma w h e n x equals fraction numerator pi over denominator 2 end fraction end subscript superscript fraction numerator k blank c o s blank x over denominator pi minus 2 x end fraction w h e n x not equal to fraction numerator pi over denominator 2 end fraction end superscript$ ’ be continuous at $chi equals fraction numerator pi over denominator 2 end fraction$ , then k=

The value of $n rightwards arrow infinity vertical line i m fraction numerator 1 minus n to the power of 2 end exponent over denominator not stretchy sum subscript blank superscript blank n end fraction$ will be

The value of $n rightwards arrow infinity vertical line i m fraction numerator 1 minus n to the power of 2 end exponent over denominator not stretchy sum subscript blank superscript blank n end fraction$ will be

parallel

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

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

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

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

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

parallel

$S plus fraction numerator 3 over denominator 2 end fraction O subscript 2 end subscript ⟶ S O subscript 3 end subscript plus 2 x k c a l$
$S O subscript 2 end subscript plus fraction numerator 1 over denominator 2 end fraction O subscript 2 end subscript ⟶ S O subscript 3 end subscript plus y k c a l$
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

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

parallel

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

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

parallel

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

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

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 $x rightwards arrow 0$ $s vertical line n x$

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

parallel

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