Lt_(x rarr oo)((x+a)/(x+b))^(x+b)= -Turito

Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent equals$

$e^{e - b}$
$e^{a + b}$
$e^{a t}$
$e^{\frac{6}{b}}$

Hint:

To solve the given function, we will use the formula $limit as x rightwards arrow infinity of left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of g left parenthesis x right parenthesis end exponent equals e to the power of stack lim with x rightwards arrow infinity below g left parenthesis x right parenthesis left parenthesis f left parenthesis x right parenthesis minus 1 right parenthesis end exponent$ after using the formula we will solve the function till that stage when putting the value of x will not make the function undefined, later we will put the value of x and get the required answer.

The correct answer is: $e to the power of e minus b end exponent$

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript space open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses to the power of x plus b end exponent w h e r e comma space f left parenthesis x right parenthesis equals open parentheses fraction numerator x plus a over denominator x plus b end fraction close parentheses space a n d space g left parenthesis x right parenthesis space equals left parenthesis x plus b right parenthesis w e space k n o w space t h a t space limit as x rightwards arrow infinity of left parenthesis f left parenthesis x right parenthesis right parenthesis to the power of g left parenthesis x right parenthesis end exponent equals e to the power of stack lim with x rightwards arrow infinity below g left parenthesis x right parenthesis left parenthesis f left parenthesis x right parenthesis minus 1 right parenthesis end exponent rightwards double arrow e to the power of limit as x rightwards arrow infinity of end exponent left parenthesis x plus b right parenthesis open parentheses fraction numerator x plus a over denominator x plus b end fraction minus 1 close parentheses rightwards double arrow e to the power of limit as x rightwards arrow infinity of end exponent open parentheses x plus b close parentheses open parentheses fraction numerator x plus a minus x minus b over denominator x plus b end fraction close parentheses rightwards double arrow e to the power of limit as x rightwards arrow infinity of end exponent left parenthesis a minus b right parenthesis rightwards double arrow e to the power of open parentheses a minus b close parentheses end exponent$

Book A Free Demo

Name*

Mobile*

+91

Email*

Grade*

I agree to get WhatsApp notifications & Marketing updates

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

Question

Hint:

Answer

The correct answer is:

Solution

Book A Free Demo

Related Questions to study

If the sides of triangles are then radius of the Circumcentre is

If the sides of triangles are then radius of the Circumcentre is

The function satisfies

The function satisfies

1, then a=

1, then a=

If a,b,c are in A.P the are in

If a,b,c are in A.P the are in

If then

If then

The quadratic equation whose roots are I and m where l = is

The quadratic equation whose roots are I and m where l = is

In

In

Let f : [-10, 10] →R, where f(x) = sin x + be an odd function. Then set of values of parameter a is/are

Let f : [-10, 10] →R, where f(x) = sin x + be an odd function. Then set of values of parameter a is/are

Light wave enters from medium 1 to medium 2. Its velocity in 2nd medium is double from 1st. For total internal reflection the angle of incidence must be greater than

Light wave enters from medium 1 to medium 2. Its velocity in 2nd medium is double from 1st. For total internal reflection the angle of incidence must be greater than

Courses

Quick Links

The correct answer is: $e to the power of e minus b end exponent$

The function $f left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript fraction numerator d t over denominator t end fraction$ satisfies

The function $f left parenthesis x right parenthesis equals stretchy integral subscript 0 end subscript superscript x end superscript fraction numerator d t over denominator t end fraction$ satisfies

$text If end text a greater than 0 text and end text L subscript x not stretchy rightwards arrow a end subscript fraction numerator a to the power of x minus x to the power of 4 over denominator x to the power of x minus a to the power of a end fraction equals negative$ 1, then a=

$text If end text a greater than 0 text and end text L subscript x not stretchy rightwards arrow a end subscript fraction numerator a to the power of x minus x to the power of 4 over denominator x to the power of x minus a to the power of a end fraction equals negative$ 1, then a=

If a,b,c are in A.P the $cot invisible function application A over 2 comma cot invisible function application B over 2 comma cot invisible function application C over 2$ are in

If a,b,c are in A.P the $cot invisible function application A over 2 comma cot invisible function application B over 2 comma cot invisible function application C over 2$ are in

If $fraction numerator b over denominator c plus a end fraction plus fraction numerator c over denominator a plus b end fraction equals 1$ then

If $fraction numerator b over denominator c plus a end fraction plus fraction numerator c over denominator a plus b end fraction equals 1$ then

In $straight triangle A B C comma left parenthesis a plus b plus c right parenthesis open parentheses tan invisible function application A over 2 plus tan invisible function application B over 2 close parentheses equals$

In $straight triangle A B C comma left parenthesis a plus b plus c right parenthesis open parentheses tan invisible function application A over 2 plus tan invisible function application B over 2 close parentheses equals$

Let f : [-10, 10] →R, where f(x) = sin x + $open square brackets fraction numerator x to the power of 2 end exponent over denominator a end fraction close square brackets$ be an odd function. Then set of values of parameter a is/are

Let f : [-10, 10] →R, where f(x) = sin x + $open square brackets fraction numerator x to the power of 2 end exponent over denominator a end fraction close square brackets$ be an odd function. Then set of values of parameter a is/are

Light wave enters from medium 1 to medium 2. Its velocity in 2^nd medium is double from 1^st. For total internal reflection the angle of incidence must be greater than

Light wave enters from medium 1 to medium 2. Its velocity in 2^nd medium is double from 1^st. For total internal reflection the angle of incidence must be greater than