If `g(x)=(f(x))/((x-a)(x-b)(x-c)),` where f(x) is a polynomial of degree `lt3,` then prove that
`(dg(x))/(dx)=|{:(1,a,f(a)(x-a)^(-2)),(1,b,f(b)(x-b)^(-2)),(1,c,f(c)(x-c)^(-2)):} |divide|{:(a^(2),a,1),(b^(2),b,1),(c^(2),c,1):}|.`

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 f(x) is a polynomial of degree <3, prove that |1af(a)//(x-a)1bf(b)//(x-b)1cf(c)//(x-c)|-:|1a a^2 1bb^2 1cc^2|=(f(x))/((x-a)(x-b)(x-c))

If g(x)=(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of degree <3 , then intg(x)dx=|1af(a)log|x-a|1bf(b)log|x-b|1cf(c)log|x-c||-:|1a a^2 1 bb^2 1 cc^2|+k (dg(x))/(dx)=|1af(a)log""(x-a)^2 1bf(b)"log"(x-b)^2 1cf(c)"log"(x-b)^2|-:|a^2a1b^2b1c^2c1| (dg(x))/(dx)=|1af(a)log""(x-a)^(-2)1bf(b)"log"(x-b)^(-2)1cf(c)"log"(x-b)^(-2)|-:|1a a^2 1bb^2 1cc^2| intg(x)dx=|1af(a)"log"|x-a|1bf(b)"log"|x-b|1cf(c)"log"|x-c||-:|a^2a1b^2b1c^2c1|+k

If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x)) where f(x) is of the form of ax^(2)+bx+c , then the value of f(1) is

If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b, then f(2) is equal to

If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b, then f(2) is equal to

Let f(x) be a polynomial such that f(-1/2)=0, then a factor of f(x) is:? (a) 2x-1 (b) 2x+1 (c) x-1 (d) x+1

If f(a,b) =(f(b)-f(a))/(b-a) and f(a,b,c)=(f(b,c)-f(a,b))/(c-a) prove that f(a,b,c)=|{:(f(a),f(b),f(c)),(1,1,1),(a,b,c):}|-:|{:(1,1,1),(a,b,c),(a^(2),b^(2),c^(2)):}| .

If f(x) = (x^n-a^n)/(x-a) , then f'(a) is a. 1 b. 1/2 c. 0 d. does not exist

If f(x)=log((1+x)/(1-x))a n dg(x)=((3x+x^3)/(1+3x^2)) , then f(g(x)) is equal to (a) f(3x) (b) {f(x)}^3 (c) 3f(x) (d) -f(x)