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

For each positive integer n,consider the point P with abscissa n on the curve y^(2)-x^(2)=1. If d_(n) represele the shortest distance from the point P to the line y=x then lim_(n rarr oo)(nd_(n)) has the value equal to

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 rarr oo)(n.d_(n)) as the value equal to (A) (1)/(2sqrt(2))(B)(1)/(2)(C)(1)/(sqrt(2)) (D) 0

Q.8 For each positive integern. consider the point P with abscissa non the curve y2 x 2 1. Ifd represents the shortest distance from the point P to the line y then Lim (n dn) has the value equal to (B) (A) 3.77 (D)0

8 For each positive inte consider the point P with abscissa non the curve 2 x2 1.Ifd, represents y the shortest distance from the point P to the line y x then Lim(n dn) as the value equal to (D) 0 (C) V2 (B)

lim_(nto oo) (2^n+5^n)^(1//n) is equal to

If x =u is a point of discontinuity of f(x)= lim_(n to oo) cos^(2n)x , then the value of cos u is

If normal at P on the curve y^2 - 3x^2 + y + 10 = 0 passes through the point (0, 3/2) ,then slope of tangent at P is n. The value of |n| is equal to

For each positive integer n, let j y_(n) =1/n ((n +1) (n +2) …(n +n) )^(1/n). For x in R, let [x] be the greatest integer less than or equal to x, If lim _( n to oo) y_(n) =L, then the value of [L] is "_________."