Home
Class 12
MATHS
Ift h ev a l u eof("lim")(nvecoo)(n^(-3/...

`Ift h ev a l u eof("lim")_(nvecoo)(n^(-3/2))dotsum_(j=1)^(6n)sqrt(j)i se q u a ltosqrt(N),t h e n` the value of `N/(12)` is __________

Text Solution

Verified by Experts

The correct Answer is:
96
`I=lim_(n to oo)( (sqrt(1)+sqrt(2)+sqrt(3)+………..+sqrt(6n))/(nsqrt(n)))`
`=lim_(nto oo) 1/n sum_(r=1)^(6n)sqrt(r/n)=int_(0)^(6)sqrt(x)dx=[2/3x^(3//2)]_(0)^(6)=2/3 . 6sqrt(6)=sqrt(96)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise JEE MAIN|12 Videos

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise JEE ADVANCED|38 Videos

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise MATRIX MATCH_TYPE|6 Videos

  • CURVE TRACING

    CENGAGE ENGLISH|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

If the value of lim_(n rarr oo)(n^(-3/2)) sum_(j=1)^(6n) sqrt(j) is equal to sqrt(N) , then the value of N/(12) is __________

T h ev a l u eof(lim)_(nvecoo)[t a npi/(2n)tan(2pi)/(2n)dottan(npi)/(2n)]^(1//n)i s e (b) e^2 (c) 1 (d) e^3

lim_(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

("lim")_(xvecoo){1/(1-n^2)+2/(1-n^2)+......n/(1-n^2)}i se q u a lto 0 (b) -1/2 (c) 1/2 (d) none of these

The value of lim_(n->oo)(sqrt(1)+sqrt(2)+sqrt(3)+.....+sqrt(n))/(nsqrt(n)) is

If f(x)=(lim)_(nvecoo)(cos(x/(sqrt(n))))^n , then the value of (lim)(xvec0)(f(x)-1)/x is 0 b. 1 c. 2 d. 3//2

The value of lim_(xrarroo)(sqrt(n^2+1)+sqrt(n))/((n^4+n)^(1/4)+4sqrt(n)) , is

If lim_(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the value of x.

("lim")_(xvec0)((1^x+2x+3^x++n^x)/n)^(1//x)i se q u a lto (n !)^n (b) (n !)^(1/n) (c) n ! (d) "ln"(n !)

If cos3 6^(@)+cot(7 1/2@)=sqrt(n_1)+sqrt(n_2)+sqrt(n_3)+sqrt(n_1)+sqrt(n_5)+sqrtn_6, then the value of sum_(i=1)^6 n_i^2 must be

Home
Profile