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

Let f(x)={(1-cos4x)/(x^2),\ \ \ if\ x 0 Determine the value of a so that f(x) is continuous at x=0.

Let f(x)={{:(cos[x]", "xle0),(|x|+a", "xlt0):}. Then find the value of a, so that lim_(xto0) f(x) exists, where [x] denotes the greatest integer function less than or equal to x.

Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is

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

Let f(x) = sin x (1+cos x) , x in (0,2pi). Find the number of critical points of f(x) . Also identify which of these critical points are points of Maxima // Minima.

If xlt0 and (2x-1)^(2)=25 , what is the value of x?

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.

f(x)={{:((1-cos2x)/(x^(2)),if x ne 0),(5, if x = 0):} at x = 0 .

if f(x) ={underset( cos x " "x ge 0)((x+lambda)^(2) " " x lt 0). find possible values of lambda such that f(x) has local maxima at x=0

Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).