Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction$

$\frac{1}{2}$
2
4
$\frac{1}{4}$

hint Hint:

We can apply L'Hopital's rule, also commonly spelled L'Hospital's rule, whenever direct substitution of a limit yields an indeterminate form. This means that the limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.
In this question, we have to find value of $Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction$ .

The correct answer is: $1 fourth$

$Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction$
We first try substitution:
$Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction$ = $Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of 4 minus 2 over denominator 4 minus 4 end fraction space equals space 0 over 0$
Since the limit is in the form 0 over 0, it is indeterminate—we don’t yet know what is it. We need to do some work to put it in a form where we can determine the limit.
$Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction$ ( L 'Hopital's Rule for zero over zero; $Lt subscript x not stretchy rightwards arrow 0 end subscript fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction space equals space fraction numerator f apostrophe left parenthesis 0 right parenthesis over denominator g apostrophe left parenthesis 0 right parenthesis end fraction$ )
$Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator open parentheses square root of x close parentheses squared minus open parentheses 2 close parentheses squared end fraction$ ( $A l s o space w e space k n o w space t h a t space Lt subscript x not stretchy rightwards arrow a end subscript fraction numerator x to the power of n space minus space a to the power of n over denominator x space minus space a end fraction space equals space n a to the power of n minus 1 end exponent$ )
Let $y space equals square root of x space end root space s o comma space y rightwards arrow 2$
$Lt subscript y not stretchy rightwards arrow 2 end subscript fraction numerator y minus 2 over denominator open parentheses y close parentheses squared minus open parentheses 2 close parentheses squared end fraction space equals space fraction numerator 1 over denominator 2 cross times 2 to the power of 2 minus 1 end exponent end fraction space equals 1 fourth$

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means $0 over 0 space o r space fraction numerator plus-or-minus infinity over denominator plus-or-minus infinity end fraction.$

A copper wire and a steel wire of same diameter and length are connected end to end a force is applied, which stretches their combined length by 1 cm, the two wires will have.....

physics-General

General

Maths-

$Lt subscript x not stretchy rightwards arrow 0 end subscript 2 over x log space left parenthesis 1 plus x right parenthesis$

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means $fraction numerator 0 over denominator 0 space end fraction space o r space fraction numerator plus-or-minus infinity over denominator plus-or-minus infinity end fraction.$

$Lt subscript x not stretchy rightwards arrow 0 end subscript 2 over x log space left parenthesis 1 plus x right parenthesis$

Maths-General

General

maths-

$T a n invisible function application left parenthesis A minus B right parenthesis plus T a n invisible function application left parenthesis B minus C right parenthesis plus T a n invisible function application left parenthesis C minus A right parenthesis equals$

maths-General

General

maths-

If $Tan invisible function application 40 to the power of ring operator plus 2 Tan invisible function application 10 to the power of ring operator equals Cot invisible function application x$ then x=

maths-General

General

maths-

If A, B, C are acute angles, $T a n invisible function application A equals 1 divided by 2$ , $T a n invisible function application B equals 1 divided by 5$ , $Tan invisible function application C equals 1 divided by 8$ then A+B+C=

maths-General

General

maths-

If $0 less than alpha comma beta less than fraction numerator pi over denominator 4 end fraction comma C o s invisible function application left parenthesis alpha plus beta right parenthesis equals fraction numerator 4 over denominator 5 end fraction comma S i n invisible function application left parenthesis alpha minus beta right parenthesis equals fraction numerator 5 over denominator 13 end fraction$ then $Tan invisible function application 2 alpha$ =

maths-General

General

maths-

If $C o s invisible function application alpha equals fraction numerator negative 12 over denominator 13 end fraction comma C o t invisible function application beta equals fraction numerator 24 over denominator 7 end fraction comma 90 to the power of ring operator end exponent less than alpha less than 180 to the power of ring operator end exponent$ and $180 to the power of ring operator end exponent less than beta less than 270 to the power of ring operator end exponent$ then the quardrant in which $alpha plus beta$ lies

maths-General

General

maths-

$Tan invisible function application 20 to the power of ring operator plus 2 Tan invisible function application 50 to the power of ring operator equals$

maths-General

General

maths-

$Tan invisible function application 20 to the power of ring operator plus Tan invisible function application 25 to the power of ring operator plus Tan invisible function application 20 to the power of ring operator Tan invisible function application 25 to the power of ring operator equals$

maths-General

General

maths-

If $Tan invisible function application 22 to the power of ring operator plus Tan invisible function application 38 to the power of ring operator minus square root of 3 equals k Tan invisible function application 22 to the power of ring operator Tan invisible function application 38 to the power of ring operator$ then k=

maths-General

General

maths-

$Lt subscript x not stretchy rightwards arrow 0 end subscript space open parentheses 1 plus fraction numerator 2 x over denominator 3 end fraction close parentheses to the power of 1 over x end exponent$

maths-General

General

physics-

Which one of the following quantities does not have unit of force per unit area.

physics-General

General

maths-

If $f left parenthesis x right parenthesis equals open curly brackets table row cell x to the power of alpha end exponent l o g invisible function application x comma end cell cell x greater than 0 end cell row cell 0 comma end cell cell x equals 0 end cell end table close$ and Rolle's theorem is applicable to f(x) for $x element of left square bracket 0 , 1 right square bracket$ then $alpha$ is equal to

maths-General

General

maths-

Given n is a positive integer for the function $f left parenthesis x right parenthesis equals 5 x left parenthesis x minus 2 right parenthesis to the power of n comma x element of left square bracket 0 comma 2 right square bracket$ , . By Rolle's theorem the value of c is 1/5 then n is equal to

maths-General

General

physics-

A medium shows relation between i and r as shown. If speed of light in the medium is nc then value of n is

physics-General

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

24

The correct answer is:

We first try substitution: = Since the limit is in the form 0 over 0, it is indeterminate—we don’t yet know what is it. We need to do some work to put it in a form where we can determine the limit. ( L 'Hopital's Rule for zero over zero; ) ( )Let

Related Questions to study

A copper wire and a steel wire of same diameter and length are connected end to end a force is applied, which stretches their combined length by 1 cm, the two wires will have.....

A copper wire and a steel wire of same diameter and length are connected end to end a force is applied, which stretches their combined length by 1 cm, the two wires will have.....

If then x=

If then x=

If A, B, C are acute angles, , , then A+B+C=

If A, B, C are acute angles, , , then A+B+C=

If then =

If then =

If and then the quardrant in which lies

If and then the quardrant in which lies

If then k=

If then k=

Which one of the following quantities does not have unit of force per unit area.

Which one of the following quantities does not have unit of force per unit area.

If and Rolle's theorem is applicable to f(x) for then is equal to

If and Rolle's theorem is applicable to f(x) for then is equal to

Given n is a positive integer for the function , . By Rolle's theorem the value of c is 1/5 then n is equal to

Given n is a positive integer for the function , . By Rolle's theorem the value of c is 1/5 then n is equal to

A medium shows relation between i and r as shown. If speed of light in the medium is nc then value of n is

A medium shows relation between i and r as shown. If speed of light in the medium is nc then value of n is

With Turito Academy.

With Turito Foundation.

Get an Expert Advice From Turito.

Turito Academy

With Turito Academy.

Test Prep

With Turito Foundation.

Courses

Quick Links

$\frac{1}{2}$
2
4
$\frac{1}{4}$

The correct answer is: $1 fourth$

If $Tan invisible function application 40 to the power of ring operator plus 2 Tan invisible function application 10 to the power of ring operator equals Cot invisible function application x$ then x=

If $Tan invisible function application 40 to the power of ring operator plus 2 Tan invisible function application 10 to the power of ring operator equals Cot invisible function application x$ then x=

If A, B, C are acute angles, $T a n invisible function application A equals 1 divided by 2$ , $T a n invisible function application B equals 1 divided by 5$ , $Tan invisible function application C equals 1 divided by 8$ then A+B+C=

If A, B, C are acute angles, $T a n invisible function application A equals 1 divided by 2$ , $T a n invisible function application B equals 1 divided by 5$ , $Tan invisible function application C equals 1 divided by 8$ then A+B+C=

Given n is a positive integer for the function $f left parenthesis x right parenthesis equals 5 x left parenthesis x minus 2 right parenthesis to the power of n comma x element of left square bracket 0 comma 2 right square bracket$ , . By Rolle's theorem the value of c is 1/5 then n is equal to

Given n is a positive integer for the function $f left parenthesis x right parenthesis equals 5 x left parenthesis x minus 2 right parenthesis to the power of n comma x element of left square bracket 0 comma 2 right square bracket$ , . By Rolle's theorem the value of c is 1/5 then n is equal to