If `a_(1), a_(2),…….a_(n)` are real numbers and the function `f(x)=(x-a_(1))^(2)+(x-a_(2))^(2)+…..+(x-a_(n))^(2)` attains its minimum value for some x = p, then p is

Let a_(1),a_(2),.......,a_(n) be fixed real numbers and define a function f(x)=(x-a_(1))(x-a_(2)) ......(x-a_(n)) , what is lim f(x) ? For some anea_(1),a_(2),.........a_(n) , compute lim_(Xrarr1) f(x)

clf a_(1),a_(2),a_(3),...,a_(n)in R then (x-a_(1))^(2)+(x-a_(2))^(2)+....+(x-a_(n))^(2) assumes its least value at x=

Let a_(1),a_(2),...,a_(n) be fixed real numbers and let f(x)=(x-a_(1))(x-a_(2))(x-a_(3))...(x-a_(n)). Find lim_(xtoa_(1))f (x). If anea_(1),a_(2),..,a_(n),Compute lim_(xtoa) f(x).

If a_(1),a_(2),...a_(n) are in H.P then the expression a_(1)a_(2)+a_(2)a_(3)+...+a_(n-1)a_(n) is equal to

If a_(1),a_(2),a_(3),dots,a_(n+1) are in A.P.then (1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))...+(1)/(a_(n)a_(n+1)) is

Let f:RrarrR be the function f(x)=(x-a_(1))(x-a_(2))+(x-a_(2))(x-a_(3))+(x-a_(3))(x-a_(1)) with a_(1),a_(2),a_(3) in R . The fix f(x)ge0 if and only if -

If a_(1),a_(2)......a_(n) are n positive real numbers such that a_(1).......a_(n)=1. show that (1+a_(1))(1+a_(2))......(1+a_(n))>=2^(n)