Let `f(x)` be a cubic polynomial in x, such that `intf(x)dx=Af'''(0)x^4+Bf''(0)x^3+Cf'(0)x^2+Df(0)+E`, where A, B, C and D are some constants and E is an arbitrary constant. Then the value of `8A+B+ C+ D` is

Let f(x)=a+b|x|+c|x|^(2) , where a,b,c are real constants. The, f'(0) exists if

Let f(x)=a+b|x|+c|x|^(2) , where a,b,c are real constants. The, f'(0) exists if

If B=int(1)/(e^(x)+1)dx=-f(x)+C , where C is the constant of integration and e^(f(0))=2 , then the value of e^(f(-1)) is

If B=int(1)/(e^(x)+1)dx=-f(x)+C , where C is the constant of integration and e^(f(0))=2 , then the value of e^(f(-1)) is

Let int(dx)/(sqrt(x^(2)+1)-x)=f(x)+C such that f(0)=0 and C is the constant of integration, then the value of f(1) is

Let int(dx)/(sqrt(x^(2)+1)-x)=f(x)+C such that f(0)=0 and C is the constant of integration, then the value of f(1) is

Let f(x) be a cubic polynomial with leading coefficient unity such that f(0)=1 and all the roots of f(x)=0 are also roots of f(x)=0. If f(x)dx=g(x)+C, where g(0)=(1)/(4) and C is constant of integration,then g(3)-g(1) is equal to

Let f(x)=a+b|x|+c|x|^(4), where a,b, and c are real constants.Then,f(x) is differentiable at x=0, if a=0( b) b=0 (c) c=0( d) none of these

Let f(x)=a+b|x|+c|x|^4 , where a ,\ b , and c are real constants. Then, f(x) is differentiable at x=0 , if a=0 (b) b=0 (c) c=0 (d) none of these