[" If "f(x)=p|sin x|+qe^(|x|)+r|x|^(3)" is "],[" differentiable at "x=0" then "p+q=]

If f(x)=p|sin x|+qe^(|x|)+r|x|^(3) and it is derivable at x=0 then which of the following is complete solution for p,p,q and r

1) Infinite 2)2 33If f(x)=p|sin x + qelxl+r|x|3 and f(x) isdifferentiable at x=0, then1) q+r=0; p is any real number2)p+q=0; r is any real number3) q=0, r=0; p is any real number4) r=0,p=0; q is any real number

If f ( x) ={(x^(p) cos((1)/(x)),x cancel=0,(0,x=0):} is differentiable at x=0, then

Show that the function f (x) = x ^(p) sin ((1)/(x)) x , ne 0, f (0) =0 is continuous but not differentiable at x=0 if 0 lt p le 1.

Let f(x)=p[x]+qe^(-[x])+r|x|^(2) , where p,q and r are real constants, If f(x) is differential at x=0. Then,

Let f(x)=p[x]+qe^(-[x])+r|x|^(2) , where p,q and r are real constants, If f(x) is differential at x=0. Then,