`a_0 f^n(x) + a_1 f^(n-1)(x).g(x) + a_2 f^(n-2) g^2(x) + ......+a_n g^n(x) >= 0`

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_(x rarr a_1)f(x) ? For some a ne a_1,a_2,....a_n , compute lim_(x rarr a)f(x) .

if f(x) = (x - a_1) (x - a_2) .....(x - a_n) then find the value of lim_(x to a_1) f(x)

Given that (1+x+x^2)^n=a_0+a_1x+a_2x^2+.....+a_(2n)x^(2n) find i) a_0 + a_1 +a_2 .. . . .+ a_(2n) ii) a_0 - a_1 + a_2 - a_3 . . . . + a_(2n) iii) (a_0)^2 - (a_1)^2 . . . . .+ (a_(2n))^2

Given that (1+x+x^2)^n=a_0+a_1x+a_2x^2+.....+a_(2n)x^(2n) find i) a_0 + a_1 +a_2 .. . . .+ a_(2n) ii) a_0 - a_1 + a_2 - a_3 . . . . + a_(2n) iii) (a_0)^2 - (a_1)^2 . . . . .+ (a_(2n))^2

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)_(x->a_1)f(x) ? For some a!=a_1,a_2,.....,a_n , compute (lim)_(x->a)f(x)

If (1 - x + x^2)^n = a_0 + a_1 x + a_2x^2 + ..... + a_(2n)x^(2n) then a_0 + a_2 + a_4 + ... + a_(2n) equals

If f(x) = lim_(n->oo) tan^(-1) (4n^2(1-cos(x/n))) and g(x) = lim_(n->oo) n^2/2 ln cos(2x/n) then lim_(x->0) (e^(-2g(x)) -e^(f(x)))/(x^6) equals