If `f_r(x),g_r(x),h_r(x),r=1,2,3` are polynomials such that `f_r(a)=g_r(a)=h_r(a),r=1,2,3a n d` `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^(prime)(x)a tx=a` is____________________

Is f(x)xx g(x)xx r(x)=LCM[f(x),g(x),r(x)]xx GCD [f(x),g(x),r(x)] ?

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that varphi(x)=|f(x)g(x)h(x)f'(x)g'(x h '(x)f' '(x)g' '(x h ' '(x)| is a constant polynomial.

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). The value of f(3) is

If f(x)=2x+3 , g(x)=1-2x and h(x)=3x. Prove that f o(g o h) = (f o g ) o h

If f(x)=2x+3, g(x) = 1-2x and h(x)=3x . Prove that f o (g o h) = (f o g) o h

Let f(x)=(x^(5)-1)(x^(3)+1),g(x)=(x^(2)-1)(x^(2)-x+1) and let h(x) be such that f(x)=g(x)h(x) . Then lim_(xto1)h(x) is

Let g^(prime)(x)>0a n df^(prime)(x) g(f(x-1)) f(g(x+1))>f(g(x-1)) g(f(x+1))

Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are differentiable functions. At some point x_0,F^(prime)(x_0)=21 F(x_0),f^(prime)(x_0)=4f(x_0),g^(prime)(x_0)=-7g(x_0), and h^(prime)(x_0)=kh(x_0) . Then k is________

If f(x), h(x) are polynomials of degree 4 and |(f(x), g(x),h(x)),(a, b, c),(p,q,r)| =mx^4+nx^3+rx^2+sx+r be an identity in x, then |(f''(0) - f''(0),g''(0) - g''(0),h''(0) -h''(0)),(a,b,c),(p,q,r)| is

If f(x)=1/x ,g(x)=1/(x^2), and h(x)=x^2 , then (A) f(g(x))=x^2,x!=0,h(g(x))=1/(x^2) (B) h(g(x))=1/(x^2),x!=0,fog(x)=x^2 (C) fog(x)=x^2,x!=0,h(g(x))=(g(x))^2,x!=0 (D) none of these