If `((2^x-1)x(x-2)^3)/(x-3)^2<0` then

Discuss extrema of the function f(x) =int_(1)^(x)2(x-1)(x-2)^(3)+3(x-1)^(2)(x-2)^(2)dx

Discuss extrema of the function f(x) =int_(l)^(x)2(x-1)(x-2)^(3)+3(x-1)^(2)(x-2)^(2)dx

Discuss extrema of the function f(x) =int_(l)^(x)2(x-1)(x-2)^(3)+3(x-1)^(2)(x-2)^(2)dx

Simplify and find the value of x: 1/((x-1)(x-2))+1/((x-2)(x-3))=2/3, x!= 1,2,3

Solve : (2x-1)(x+3)(x-2)(2x+3)+ 20 =0

If f(x)=(2x+1)/(2x^(3)+3x^(2)+x) and S={x:f(x)>0} then s contains (a) (-oo,-(3)/(2))(b)(-(3)/(2),-(1)/(4))(c)(-(1)/(4),(1)/(2)) (d) ((1)/(2),3)

(x^(2)-x)-(1)/(2)(x-3+3x^(2))

Check whether the following are quadratic equations : (1) (x-1)^(2)=2(x-3) (2) x^(2)-2x=(-2)(3-x) (3) (x-2)(x+1)=(x-1)(x+3) (4) (x-3)(2x+1)=x(x+5) (5) (2x-1)(x-3)=(x+5)(x-1) (6) x^(2)+3x+1=(x-2)^(2) (7) (x+2)^(3)=2x(x^(2)-1) (8) x^(3)-4x^(2)-x+1=(x-2)^(3)

Find the sum to n terms of the sequence : (i) (x+1/x)^(2)+ (x^(2)+1/x^(2))^(2)+ (x^(3)+1/x^(3))^(2) ... to n terms (ii) (x+y)+ (x^(2)+xy+y^(2))+(x^(3)+x^(2)y+xy^(2)+y^(3)) , ... to n terms

Find the intervals in which the following functions are positive and in which they are negative f(x) = ( x - 1)^(2) ( x + 2)^(3) ( x - 3)^(4) x^(2) ( 4 - x)