`f(x)=sin[x]+[s in x],0

What is the fundamental period of f(x) = (sin x+ sin 3x)/(cos x+ cos 3x)

Find f'(x)" if "f(x)= (sin x)^(sin x) for all 0 lt x lt pi .

f(x)=sin^-1x +|sin^-1x| +sin^-1|x| no. of solution of equation f(x)=x is

If f(x)={{:((sin[x])/([x])","" ""for "[x]ne0),(0","" ""for "[x]=0):} where [x] denotes the greatest integer less than or equal to x. Then find lim_(xto0)f(x).

Consider function f(x) = sin^(-1) (sin x) + cos^(-1) (cos x), x in [0, 2pi] (a) Draw the graph of y = f (x) (b) Find the range of f(x) (c) Find the area bounded by y = f(x) and x-axis

find the maximum value of f(x) = (sin^(-1) (sin x))^(2) - sin^(-1) (sin x)

Which of the following function is not differentiable at x=0? f(x)=min{x ,sinx} f(x)={0,xgeq0x^2,x<0 f(x)= x^2 sgn(x)

Let f_1:R→R,f_2:[0,∞)→R, f_3:R→R and f_4:R→[0,∞) be defined by f_1(x)={ ∣x∣ if x<0 ; e^x if x≥0 ; f_2(x)=x^2 ; f_3(x)={ sin x if x<0 ; x if x≥0 ; f_4(x)={ f_2(f_1(x)) if x<0 f_2(f_1(x)) if x≥0 ​then f_4 is

Examine the continuity of f, where f is defined by f(x)={{:(sin x-cos x," if "x ne 0),(-1," if "x= 0):} .

If F(x)=[("cos"x,-sin x,0),(sin x,cos x,0),(0,0,1)] and G(y)=[(cos y,0,sin y),(0,1,0),(-sin y,0,cos y)] , then [F(x) G(y)]^(-1) is equal to