If ` |(e^x,sin x),(cos x, ln(1+x))|= A+Bx+Cx^2+...` then find the value of A and B

If [{:(,e^(x),sin x),(,cos x,ln(1+x))]:}=A+Bx+Cx^(2)+....... then find the value of A and B.

If [{:(,e^(x),sin x),(,cos x,ln(1+x))]:}=A+Bx+Cx^(2)+....... then find the value of A and B.

If the function f(x) is continuous at x=0, where f(x) ={((log(1+Ax))/x-3, "if " x lt0), (5, "if " x = 0), ((e^(Bx)-1+sin4x)/x, "if " x gt 0):} Then, find the values of A and B.

If Delta(x)=|((e^x,sin2x,tanx^2)),((In(1+x),cosx,sinx)),((cosx^2,e^x-1,sinx^2))|=A+Bx+Cx^2+.... then B is equal to

If Delta(x)=|((e^x,sin2x,tanx^2)),((In(1+x),cosx,sinx)),((cosx^2,e^x-1,sinx^2))|=A+Bx+Cx^2+.... then B is equal to

If Delta(x)=|((e^x,sin2x,tanx^2)),((In(1+x),cosx,sinx)),((cosx^2,e^x-1,sinx^2))|=A+Bx+Cx^2+.... then B is equal to

If (2cos x-sin x+lambda)/(cos x+sin x-2)dx=A ln|cos x+sin x-2|+Bx+C then the value of A+B+| lambda| is

If y=(sin x)^(ln x)cos ec(e^(x)(a+bx)) and a+b=(pi)/(2e) then the value of (dy)/(dx) at x=1 is (sin1)ln sin(1)(b)0ln sin(1)(d)1+ln(sin1)

If x satisfies the cubic equation ax^(3)+bx^(2)+cx+d=0 such that cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x)=pi , then find the value of (b+c)-(a+d) .