Let `f(x)={x^2 cos(1/x) , x lt 0 and 0 , x=0 and x^2 sin(1/x) , xlt 0` then which of the following is (are) correct?

f(x)={x^(2)cos((1)/(x)),x<0 and 0,x=0 and x^(2)sin((1)/(x)),x<0 then which of the following is (are) correct?

Let f(x) be a non negative continuous and bounded function for all xge0 .If (cos x)f(x) lt (sin x- cosx)f(x) forall x ge 0 , then which of the following is/are correct?

Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln (ax ^(2)+ bx +c))/(x ^(2)),,, -1 le x lt 0),(1 ,,, x =0),((sin (e ^(x ^(2))-1))/(x ^(2)),,, 0 lt x le 1):} Then which of the following is/are corrent

Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln (ax ^(2)+ bx +c))/(x ^(2)),,, -1 le x lt 0),(1 ,,, x =0),((sin (e ^(x ^(2))-1))/(x ^(2)),,, 0 lt x le 1):} Then which of the following is/are corrent

Let the function f, g and h be defined as follows: f(x)={xsin(1/x) for -1<=x<=1 and x != 0 and 0 for x=0 and g(x)={x^2sin(1/x) for -1<=x<=1 and x !=0, 0 for x=0 h(x)=|x|^3 for -1<=x<=1 Which of the following is/are true?

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}