" Let "f(x)={[1+sin x,x<0],[x_(2)-x+1,x>0]

Let f(x)={1+sin x,x =0

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

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

Let f(x)=sin x,x =0 then

Let f(x)=x sin pi x,x>0 Then for all natural numbers n,f(x) vanishes at

Let f(x)={(1+sin(x), if x lt 0), (x^2-x+1, if x >= 0):}, then: (a) f has local maximum at x=0, (b). f has local minimum at x=0, (c) f is increasing everywhere, (d) f is decreasing everywhere.

Let f(x)={[sin(pi x)/(2),0 =1] ,then check continuity at x=1

Let f(x)=1+x.sin x*[cos x]*0

Let f (x) = {{:((1+sin x )",", when, 0 le x lt (pi)/(2)), (" " 1",", when, x lt 0 ):} Show that f ' (0) does not exist.

Let f(x)= [[cos x, -sin x, 0],[sin x, cos x, 0],[0,0,1]] ,Show that f (x) f(y)= f(x+y) .