(x)/(1x)(a+b)^(3)-8(a-b)^(3)

If a, b and c be the roots of 3 x^(3)+8 x+7=0 , then the value of (a+b)^(3)+(b+c)^(3)+(c+a)^(3) is equal to

A : (a-b)/(a)+(1)/(2)((a-b)/(a))^(2)+(1)/(3)((a-b)/(a))^(3)+....=log_(e)((a)/(b)) R : log_(e)(1-x)=-x-(x^(2))/(2)-(x^(3))/(3)-(x^(4))/(4)-....

Given "^(8)C_(1)x(1-x)^(7)+2*^(8)C_(2)x^(2)(1-x)^(6)+3*^(8)C_(3)x^(3)(1-x)^(5)+...+8*x^(8)=ax+b , then a+b is (a) 4 (b) 6 (c) 8 (d) 10

let f(x)=-x^(3)+(b^(3)-b^(2)+b-1)/(b^(2)+3b+2) if x is 0 to 1 and f(x)=2x-3 if x if 1 to 3. All possible real values of b such that f(x) has the smallest value at x=1 are

If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))| = (a - b) (b - c) (c - a) (a + b + c) , where a,b,c are all different, then the determinant |(1,1,1),((x-a)^(2),(x-b)^(2),(x-c)^(2)),((x-b)(x-c),(x-c)(x-a),(x-a)(x-b))| vanishes when a)a + b + c = 0 b) x = (1)/(3) (a + b + c) c) x = (1)/(2) (a + b + c) d) x = a + b + c

Let a,b,c be such that (1)/((1-x)(1-2x)(1-3x))=(a)/(1-x)+(b)/(1-2x)+(c)/(1-3x) then (a)/(1)+(b)/(3)+(c)/(5)

If lim_(x rarr oo)((1+a^(3))+8e^((1)/(x)))/(1+(1-b^(3))e^((1)/(x)))=2, then there

lim_(x to0) ((1+a^(3))+8e^(1//x))/(1+(1-b^(3))e^(1//x))=2 " then "-

{(x){(1-sin^(2)x)/(3cos^(2)x),x (pi)/(2) then f(x) is continuous at x=(pi)/(2), if (a)a=(1)/(3),b=2 (b) a=(1)/(3),=(8)/(3)(c)a=(2)/(3),b=(8)/(3)(d) none of these