Solution for the question - General 0log 4 '/>1log 2 '/>

Maths-

General

Easy

Question

$L t subscript left parenthesis x rightwards arrow 0 right parenthesis left parenthesis x times 2 to the power of x minus x right parenthesis divided by left parenthesis 1 minus c o s invisible function application x right parenthesis$

$\log 2$
1
$\log 4$
0

hint Hint:

We are given a function. We have to take its limit. While taking the limit we have to careful that the value doesn't become zero on substitution.

The correct answer is: $log invisible function application 4$

The given function is
$f open parentheses x close parentheses equals fraction numerator open parentheses x times 2 to the power of x minus x close parentheses over denominator 1 minus cos x end fraction$
We have to take the limit of this function.
$limit as x rightwards arrow 0 of f open parentheses x close parentheses equals limit as x rightwards arrow 0 of fraction numerator x 2 to the power of x minus x over denominator 1 space minus space cos x end fraction space space space space space space space space space space space space space space equals space limit as x rightwards arrow 0 of fraction numerator x left parenthesis 2 to the power of x minus 1 right parenthesis over denominator 1 end fraction cross times fraction numerator 1 over denominator 1 minus cos x end fraction space space space space space space space space space space space space space space equals limit as x rightwards arrow 0 of fraction numerator x left parenthesis 2 to the power of x minus 1 right parenthesis over denominator 1 end fraction cross times fraction numerator 1 over denominator 2 sin squared begin display style x over 2 end style end fraction space space space space space space space space space space... left curly bracket cos 2 A space equals space 1 space minus 2 sin squared A right curly bracket space N o w comma space w e space h a v e space t w o space f o r m u l a s limit as x rightwards arrow 0 of fraction numerator a to the power of x minus 1 over denominator x end fraction equals log a space space space space a n d space limit as x rightwards arrow 0 of fraction numerator A over denominator S i n A end fraction equals space 1 space space space space space space$
We will adjust the the given function in a way to get a above formula for simplification.
$limit as x rightwards arrow 0 of f left parenthesis x right parenthesis space equals space limit as x rightwards arrow 0 of fraction numerator x left parenthesis 2 to the power of x minus 1 right parenthesis over denominator open parentheses begin display style x over 2 end style close parentheses squared end fraction cross times fraction numerator open parentheses begin display style x over 2 end style close parentheses squared over denominator 2 sin squared begin display style x over 2 end style end fraction space space space space space space space space space space space space space space space equals space limit as x rightwards arrow 0 of fraction numerator x left parenthesis 2 to the power of x minus 1 right parenthesis over denominator begin display style x squared over 4 end style end fraction cross times 1 half cross times open parentheses fraction numerator begin display style x over 2 end style over denominator sin begin display style x over 2 end style end fraction close parentheses squared space space space space space space space space space space space space space space space equals limit as x rightwards arrow 0 of fraction numerator 4 left parenthesis 2 to the power of x minus 1 right parenthesis over denominator x end fraction cross times 1 half cross times open parentheses fraction numerator begin display style x over 2 end style over denominator sin begin display style x over 2 end style end fraction close parentheses squared space space space space space space space space space space space space space space space equals space space space 4 space left parenthesis log 2 right parenthesis space cross times 1 half cross times left parenthesis 1 right parenthesis squared space space space space space space space space space space space space space space space equals 2 log 2 space space space space space space space space space space space space space space space space equals log 2 squared space space space space space space space space space space space space space space space equals log 4 space space space space space space space$
This is the final answer.

For such questions, we should know different formulas of limits.

$L t left parenthesis x rightwards arrow pi divided by 2 right parenthesis left parenthesis s e c invisible function application x minus t a n invisible function application x right parenthesis divided by left parenthesis pi divided by 2 minus x right parenthesis$

Maths-General

General

Maths-

$L t subscript left parenthesis x rightwards arrow pi divided by 2 right parenthesis left square bracket s e c invisible function application 3 x c o s invisible function application 5 x right square bracket$

For such questions, we should know different formulas of limits. We should know L'Hospitals rule to solve question.

$L t subscript left parenthesis x rightwards arrow pi divided by 2 right parenthesis left square bracket s e c invisible function application 3 x c o s invisible function application 5 x right square bracket$

Maths-General

For such questions, we should know different formulas of limits. We should know L'Hospitals rule to solve question.

General

Maths-

$L t left parenthesis x rightwards arrow pi divided by 2 right parenthesis left square bracket s e c 3 x c o s 5 x right square bracket$

Maths-General

General

Chemistry-

K₁and K₂ are equilibrium constants for reaction (i) and (ii)
$N subscript 2 end subscript left parenthesis g right parenthesis plus O subscript 2 end subscript left parenthesis g right parenthesis ℶ 2 N O left parenthesis g right parenthesis$ (i) $N O left parenthesis g right parenthesis 1 divided by 2 N subscript 2 end subscript left parenthesis g right parenthesis plus 1 divided by 2 O subscript 2 end subscript left parenthesis g right parenthesis minus$ (ii) Then,

Chemistry-General

General

Maths-

$L t left parenthesis x rightwards arrow 0 left parenthesis x plus 2 right parenthesis plus 4 right parenthesis left parenthesis 3 left parenthesis x plus 1 right parenthesis plus 4 right parenthesis divided by 3 left parenthesis x plus 2 right parenthesis$

Maths-General

General

Maths-

$left parenthesis L t left parenthesis x rightwards arrow 0 right parenthesis left parenthesis sin hat left parenthesis negative 1 right parenthesis x right parenthesis divided by x right parenthesis right parenthesis$

Maths-General

General

Maths-

$L t left parenthesis x rightwards arrow 0 right parenthesis 2 x divided by left parenthesis t a n negative 1 right parenthesis x right parenthesis$

Maths-General

General

Maths-

$L t left parenthesis x rightwards arrow 4 right parenthesis left parenthesis √ x minus 2 right parenthesis divided by left parenthesis x minus 4 right parenthesis$

Maths-General

General

Maths-

$L t left parenthesis x rightwards arrow 0 right parenthesis 2 divided by x l o g left parenthesis 1 plus x right parenthesis$

Maths-General

General

Maths-

$L t left parenthesis x rightwards arrow 0 right parenthesis left parenthesis 1 plus 2 x divided by 3 right parenthesis left parenthesis 1 divided by x right parenthesis$

Maths-General

General

Maths-

$Lt subscript straight x not stretchy rightwards arrow negative 1.5 end subscript COS to the power of negative 1 end exponent open parentheses fraction numerator straight x plus 3 over denominator 3 end fraction close parentheses$

Maths-General

General

Maths-

$L t left parenthesis x rightwards arrow 2 right parenthesis l o g subscript 1 0 left square bracket x to the power of 6 plus √ left parenthesis x squared plus 1292 right parenthesis right square bracket$

Maths-General

General

Maths-

$L t left parenthesis x rightwards arrow 0 right parenthesis left parenthesis 1 minus c o s x right parenthesis divided by left parenthesis x rightwards arrow 0 right parenthesis 1 divided by x squared$

Maths-General

General

Maths-

$L t left parenthesis x rightwards arrow 0 right parenthesis left parenthesis 3 s i n x to the power of 0 minus s i n 3 x to the power of 8 right parenthesis divided by x cubed$

Maths-General

General

Maths-

$L t left parenthesis x rightwards arrow 0 right parenthesis left parenthesis left parenthesis 1 plus x right parenthesis left parenthesis 1 divided by 5 right parenthesis minus left parenthesis 1 minus x right parenthesis left parenthesis 1 divided by 2 right parenthesis right parenthesis divided by x$

Maths-General

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10

We are given a function. We have to take its limit. While taking the limit we have to careful that the value doesn't become zero on substitution.

The correct answer is:

The given function isWe have to take the limit of this function.We will adjust the the given function in a way to get a above formula for simplification.This is the final answer.

Related Questions to study

K1 and K2 are equilibrium constants for reaction (i) and (ii) (i) (ii) Then,

K1 and K2 are equilibrium constants for reaction (i) and (ii) (i) (ii) Then,

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$\log 2$
1
$\log 4$
0

The correct answer is: $log invisible function application 4$