Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

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 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: $e to the power of e minus b end exponent$

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

Related Questions to study

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of x minus e to the power of s in space x end exponent over denominator 2 left parenthesis x minus sin space x right parenthesis end fraction equals$

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator e to the power of x minus e to the power of s in space x end exponent over denominator 2 left parenthesis x minus sin space x right parenthesis end fraction equals$

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

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

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator open parentheses 1 minus e to the power of x close parentheses sin begin display style space end style x over denominator x squared plus x cubed end fraction equals$

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator open parentheses 1 minus e to the power of x close parentheses sin begin display style space end style x over denominator x squared plus x cubed end fraction equals$

parallel

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 then $c o t A over 2 comma c o t B over 2 a n d space c o t C over 2$ are in

If a,b,c are in A.P then $c o t A over 2 comma c o t B over 2 a n d space c o t C over 2$ are in

parallel

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x left parenthesis 1 plus a cos invisible function application x right parenthesis minus b sin invisible function application x over denominator x cubed end fraction equals 1 text then end text straight a equals comma straight b equals$

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x left parenthesis 1 plus a cos invisible function application x right parenthesis minus b sin invisible function application x over denominator x cubed end fraction equals 1 text then end text straight a equals comma straight b equals$

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x 10 to the power of x minus x over denominator 1 minus cos space x end fraction equals$

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x 10 to the power of x minus x over denominator 1 minus cos space x end fraction equals$

$L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator n open parentheses 1 cubed plus 2 cubed plus midline horizontal ellipsis times plus n cubed close parentheses squared over denominator open parentheses 1 squared plus 2 squared plus midline horizontal ellipsis plus n squared close parentheses cubed end fraction equals$

$L t subscript n not stretchy rightwards arrow straight infinity end subscript fraction numerator n open parentheses 1 cubed plus 2 cubed plus midline horizontal ellipsis times plus n cubed close parentheses squared over denominator open parentheses 1 squared plus 2 squared plus midline horizontal ellipsis plus n squared close parentheses cubed end fraction equals$

parallel

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

$Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator 1 over denominator sin squared begin display style space end style x end fraction minus fraction numerator 1 over denominator sinh squared space x end fraction equals$

$Lt subscript x not stretchy rightwards arrow 0 end subscript space fraction numerator 1 over denominator sin squared begin display style space end style x end fraction minus fraction numerator 1 over denominator sinh squared space x end fraction equals$

The quadratic equation whose roots are I and m where l = $lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 3 sin space theta minus 4 sin cubed space theta over denominator theta end fraction close parentheses m equals lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 2 tan space theta over denominator theta open parentheses 1 minus tan squared space theta close parentheses end fraction close parentheses$ is

The quadratic equation whose roots are I and m where l = $lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 3 sin space theta minus 4 sin cubed space theta over denominator theta end fraction close parentheses m equals lim for theta not stretchy rightwards arrow 0 of open parentheses fraction numerator 2 tan space theta over denominator theta open parentheses 1 minus tan squared space theta close parentheses end fraction close parentheses$ is

parallel

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

physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.