Home
Class 12
MATHS
Evaluate: ("lim")(xvecoo)(1+1/(a+b x))^(...

Evaluate: `("lim")_(xvecoo)(1+1/(a+b x))^(c+dx)` ,where a, b, c and d are positive

A

`e^(d//b)`

B

`e^(c//a)`

C

`e^((c+d)//(a+b))`

D

e

Text Solution

Verified by Experts

The correct Answer is:
A
`L=lim_(x to oo) (1+(1)/(a+bx))^(c+dx) " "["form "1^(oo)]`
`=e^(lim_(x to oo)(c+dx)/(a+bx))=e^(lim_(x to oo) (c//x+d)/(a//x+b))=e^((0+d)/(0+b))=e^(d//b)`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS)|60 Videos

  • CIRCLE AND CONICS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise All Questions|74 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

Similar Questions

Explore conceptually related problems

Evaluate: lim_(x rarr oo)(1+(1)/(a+bx))^(c+dx), where a,b,c and dare positive , where

Evaluate the following limits: (lim)_(x->oo)(1+1/(a+b x))^(c+dx)w h e r e\ a ,\ b ,\ c\ a n d\ d are positive.

The minimum value of an expression (a+b+c+d)((3)/(b+c+d)+(3)/(c+d+a)+(3)/(d+a+b)+(3)/(a+b+c)) is,where a,b,c and d are positive numbers.

If f(x)=a+bx^(2)+cx^(4)+dx^(6), where a,b,c,d all are positive constants, then

If the zero of the polynomial p(x)=8x^(3)-3x^(2)-3x-1 can be written in the form of (a^((1)/(3))+b^((1)/(3))+1)/(c) .where a,b and c are positive integers,then

If log_(b) a. log_(c ) a + log_(a) b. log_(c ) b + log_(a) c. log_(b) c = 3 (where a, b, c are different positive real number ne 1 ), then find the value of a b c.

prove "lim"_(xvecoo)(ln x)/([x])="lim"_(xvecoo)([x])/(ln x) where [.] is G.I.F. & {.} denotes fractional part function

The value of (lim)_(xvecoo)[tan^(-1)(x+1)/(x+2)-dotpi/4],w h e r e[x] denotes greatest integer lt=x , is 1/2 b. -1/2 c.1 d. -1

If 49392=a^(4)b^(2)c^(3), find the value of a,b and c, where a,b and c are different positive primes.