If `f(x)={-(cos^2pix)/2,0lt=x<1(1-x)^2,0lt=xlt=2` the number of values of `' c '` obtained by applying LMVT on `f(x)` in interval [0, 2] is 1 (b) 2 (c) 3 (d) LMVT is not applicable

If f(x)={("sin"(pix)/2,, x lt1),(4x-3,,1lexle2),(log2(2x^(2)-4),,2ltxlt3):} then value of lim_(xto1)f(x)+lim_(xto2^(+))f(x) is

Let f(x)={sin(pix)/2,0lt=x<1 3-2x ,xgeq1 f(x) has local maxima at x=1 f(x) has local minima at x=1 f(x) does not have any local extrema at x=1 f(x) has a global minima at x=1

The number of point f(x) ={{:([ cos pix],0le x lt1),( |2x-3|[x-2],1lt xle2):} is discontinuous at Is ([.] denotes the greatest intgreal function )

f(x)={cos(pix)/2,x >0, x+a ,xlt=0 Find the values of a if x=0 is a point of maxima.

f(x)={cos(pix)/2,x >0 x+a ,xlt=0 Find the values of a if x=0 is a point of maxima.

If f (x)= [{:( cos x ^(2),, x lt 0),( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where f (x) =f )|x|) is non-difierentiable.

Given f(x) is a periodic function with period 2 and it is defined as " "f(x) = {{:([cos""(pix)/(2)]+1",",,0lt x lt 1), (2-x",",,1 le x lt 2):} Here [*] represents the greatest integer le x . If f(0)=1 , then draw the graph of the function for x in [-2, 2] .

If f(x) = {{:("sin"(pix)/(2)",",x lt 1),([x]",",x ge 1):} , where [x] denotes the greatest integer function, then

If f(x)=cos{(pi)/(2)[x]-x^(3)},1 lt x lt 2and[x]= the greatest integer lex , then find f'(root(3)((pi)/(2)))

In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where g (x) =f (|x|) is non-differentiable.