If `f(x)` is a polynomial of degree `<3,` then, `f(x)/((x−a)(x−b)(x−c))​`is equals to

Let f(x)=(x^3+2)^(30) If f^n (x) is a polynomial of degree 20 where f^n(x) denotes the n^(th) derivativeof f(x) w.r.t x then then value of n is

If int(tan^(9)x)dx=f(x)+log|cosx|, where f(x) is a polynomial of degree n in tan x, then the value of n is

Evaluate: intf(x)/(x^3-1)dx , where f(x) is a polynomial of degree 2 in x such that f(0)=f(1)=3f(2)=-3

If int(f(x))/(x^(3)-1)dx , where f(x) is a polynomial of degree 2 in x such that f(0)=f(1)=3f(2)=-3 and int(f(x))/(x^(3)-1)dx=-log|x-1|+log|x^(2)+x+1|+(m)/(sqrt(n))tan^(-1)((2x+1)/(sqrt(3)))+C . Then (2m+n) is

If g(x)=(f(x))/((x-a)(x-b)(x-c)) ,where f(x) is a polynomial of degree <3 , then intg(x)dx=|[1,a,f(a)log|x-a|],[1,b,f(b)log|x-b|],[1,c,f(c)log|x-c|]|-:|[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|+k (dg(x))/(dx)=|[1,a,-f(a)(x-a)^(-2)],[1,b,-f(b)(x-b)^(-2)],[1,c,-f(c)(x-c)^(-2)]|:-|[1,a,a^2],[1,b,b^2],[1,c,c^2]|

If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree 0 b. 1 c. 2 d. 3

If a^2+b^2+c^2=-2\ a b n df(x)=|1+a^xx(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree- a. 2 b. \ 3 c. \ 0 d. 1

Let f:[0,1] to [0,1/2] be a function such that f(x) is a polynomial of 2nd degree, satisfty the following condition : (a) f(0)=0 (b) has a maximum value of 1/2 at x=1 . If A is the area bounded by y=f(x)=f^(-1)(x) and the line 2x+2y-3=0 in 1st quadrant, then the value of 24A is equal to "......" .

sqrt(2) is a polynomial of degree

If f(x) g(x) and h(x) are three polynomials of degree 2 and Delta = |( f(x), g(x), h(x)), (f'(x), g'(x), h'(x)), (f''(x), g''(x), h''(x))| then Delta(x) is a polynomial of degree (dashes denote the differentiation).