Home
Class 12
MATHS
For each positive integer n gt a,A(n) re...

For each positive integer `n gt a,A_(n)` represents the area of the region restricted to the following two inequalities : `(x ^(2))/(n ^(2)) + y ^(2) and x ^(2)+ (y ^(2))/(n ^(2)) lt 1.` Find `lim _(n to oo) A_(n).`

A

4

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • AREA UNDER CURVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|4 Videos

  • AREA UNDER CURVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|6 Videos

  • APPLICATION OF DERIVATIVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|22 Videos

  • BIONMIAL THEOREM

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|16 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following limits : Lim_(n to oo) (1+2+3+...+n)/(n^(2)) ( or Lim_(x to oo) (Sigman)/(n^(2)))

Find the indicated terms in each of the following sequences whose n^(th) terms are a_(n) = (a_(n-1))/(n^(2)) , (n ge 2) , a_(1) =3 , a_(2) , a_(3)

Find a_(1) and a_(9) if a_(n) is given by a_(n) = (n^(2))/(n+1)

Evaluate the following limit: (lim)_(n->oo)(1/(n^2)+2/(n^2)+3/(n^2)++(n-1)/(n^2\ ))

Find the first five terms of the following sequences and write down the corresponding series (i) a_(n) = (1)/(5) (2n -3) (ii) a_(1) =a_(2) = 1 , a_(n) = a_(n-1) + a_(n-2) , n gt 2

For each positive integer consider the point P with abscissa n on the curve y^2-x^2=1. If d_n represents the shortest distance from the point P to the line y=x then lim_(n->oo)(nd_n) has the value equal to:

For each positive integer n , let y_n=1/n((n+1)(n+2)dot(n+n))^(1/n) For x in R let [x] be the greatest integer less than or equal to x . If (lim)_(n->oo)y_n=L , then the value of [L] is ______.

Evaluate the following limit: (lim)_(n->oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

Let n be positive integer such that, (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then a_(r) is :

If x and y are positive real numbers and m, n are any positive integers, then prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt 1/4