Greatest integral x satisfying `sqrt(4-x^2)+|x|/xge0`

Draw the graph of the function, f(x)=sqrt(x)(xge0) .

Find the feasible region satisfying the inequation 2x+yle4,xge0,yge0 .

Let f(x) be a continuous function which takes positive values for xge0 and satisfy int_(0)^(x)f(t)dt=x sqrt(f(x)) with f(1)=1/2 . Then

Let f(x) be a continuous function which takes positive values for xge0 and satisfy int_(0)^(x)f(t)dt=x sqrt(f(x)) with f(1)=1/2 . Then

Shade the feasible region satisfying ineuations x+2yle10 , x+yge1 , x-ylt0 and xge0, yge0 .

Let denote the greatest integer less than or equal to x. For example : = 5 and = 3 . Now, which column below is larger? {:("Column A",xge0,"Column B),(sqrt(x), ,x):}

Let f(x)={(cos[x],xge0),(|x|+a,xlt0):} (where [.] denotes greatest integer function) If lim_(xto0)f(x) exists then a is: