" 32.Show that the function fgiven by "f(x)=tan^(-1)(sin x+cos x),x>0

Show that the function f given by f(x) = tan^(-1)(sin x + cos x), x gt 0 is always an strictly increasing functions in (0, (pi)/(4))

Show that the function f given by f(x)=tan^(-1)(sin x + cos x), x gt 0 is always an increasing function in (0, (pi)/(4)) .

Show that the function f given by f(x) = tan^(-1) (sin x+cosx ) , x gt 0 is always an increasing function in (0,(pi)/(4)) .

Show that the function f given by f(x) = tan^(-1) (sin x+cosx ) , x gt 0 is always an increasing function in (0,(pi)/(4)) .

Show that the function fgivenbyf(x)=tan^(-1)(sin x+cos x)x>0 is always an strictly increasing function in (0,(pi)/(4))

Show that the function f(x) given by f(x)={(sin x)/(x)+cos x,x!=0 and 2,x=0 is continuous at x=0

Show that the function f(x) given by f(x)={:{(x" sin "(1)/(x)", if "x!=0),(0" , if "x=0):} is continuous at x =0

Show that the functions f(x) given by f(x)={x(sin1)/(x),quad x!=00,quad x=0 is continuous at x=0

Find the intervals in which the function fgiven by f(x)=(4sin x-2x-x cos x)/(2+cos x) is (i) increasing (ii) decreasing.

Show that function f(x) given by f(x)={(x sin(1/x),,,x ne 0),(0,,,x=0):} is continuous at x=0