If `f(x)=(h_1(x)-h_1(-x))(h_2(x)-h_2(-x))...(h_(2n+1)(x)-h_(2n+1)(-x))` and `f(200)=0,` then prove that `f(x)` is many one function.

If f(x)= x^2 , then (f(x+h)-f(x))/(h) =

Given g(x)=(1/x), h(x)=x^(2)+2x+(lamda+1) and u(x)=1/x+cos(1/(x^(2))) Let f(x)=lim_(ntooo)(x^(2n+1)g(x)+h(x))/(x^(2n)+3x.u(x)) If lim+(xto2)f(x)=I , then [I] (where [.] denotes the greatest integer function), is equal to :

If f_(r)(x), g_(r)(x), h_(r) (x), r=1, 2, 3 are polynomials in x such that f_(r)(a) = g_(r)(a) = h_(r) (a), r=1, 2, 3 and " "F(x) =|{:(f_(1)(x)" "f_(2)(x)" "f_(3)(x)),(g_(1)(x)" "g_(2)(x)" "g_(3)(x)),(h_(1)(x)" "h_(2)(x)" "h_(3)(x)):}| then F'(x) at x = a is ..... .

If f is twice differentiable such that f''(x)=-f(x), f'(x)=g(x), h'(x)=[f(x)]^(2)+[g(x)]^(2) and h(0)=2, h(1)=4, then the equation y=h(x) represents.

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xy(x)= 1 (b) -1 (c) 0 (d) none of these

If f(x)=x-1, g(x)=3x , and h(x)=5/x , then f^(-1)(g(h(5))) =

If g(x)=(2h(x)+|h(x)|)/(2h(x)-|h(x)|) where h(x)=sinx-sin^n x ,n in R^+, the set of positive real numbers, and f(x)={[g(x)],x(0,pi/2)uu(pi/2,pi) and 3,x=pi/2 where [.] denotes greatest integer function. Then (a) f(x) is continuous and differentiable at x=pi/2, when 0ltnlt1 (b) f(x) is continuous and differentiable at x=pi/2, when ngt1 (c) f(x) is discontinuous and non differentiable at x=pi/2,for0ltnlt1 (d) f(x) is continuous but not differentiable at x=pi/2, when ngt1

If Delta_(f)H^(@)(C_(2)H_(4)) and Delta_(f)H^(@)(C_(2)H_(6)) are x_(1) and x_(2) kcal mol^(-1) , then heat of hydrogenation of C_(2)H_(4) is :

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (b) -1 (c) 0 (d) none of these

If int(dx)/(x+x^(2011))=f(x)+C_(1) and int(x^(2009))/(1+x^(2010))dx=g(x)+C_(2) (where C_(1) and C_(2) are constants of integration). Let h(x)=f(x)+g(x). If h(1)=0 then h(e) is equal to :