For tha function `f(x)=(pi-x)(cosx)/(|sinx|); x!=pi and f(pi)=1,` which of the following statement is/are true :

Consider the following statements : 1. The function f(x)=sinx decreases on the interval (0,pi//2) . 2. The function f(x)=cosx increases on the interval (0,pi//2) . Which of the above statements is/are correct ?

If f(x)=(1-cosx)/(1-sinx)," then: "f'((pi)/(2)) is

Consider the real - valued function satisfying 2f(sinx) + f(cosx) = x . Then , which of the following is not true ? a)Domain of f(x) is [-1,1] b)Range of f(x) is [-(2pi)/3,pi/3] c)f(x) is one - one d)None of these

Let f:(0, pi)->R be a twice differentiable function such that (lim)_(t->x)(f(x)sint-f(x)sinx)/(t-x)=sin^2x for all x in (0, pi) . If f(pi/6)=-pi/(12) , then which of the following statement(s) is (are) TRUE? f(pi/4)=pi/(4sqrt(2)) (b) f(x)<(x^4)/6-x^2 for all x in (0, pi) (c) There exists alpha in (0, pi) such that f^(prime)(alpha)=0 (d) f"(pi/2)+f(pi/2)=0

Show that the function f(x)=|sinx+cosx| is continuous at x=pi .

If f(x)=(2-3cosx)/(sinx) , then f'((pi)/(4)) is equal to

Let f:(0,pi) rarr R be a twice differentiable function such that lim_(t rarr x) (f(x)sint-f(t)sinx)/(t-x) = sin^(2) x for all x in (0,pi) . If f((pi)/(6))=(-(pi)/(12)) then which of the following statement (s) is (are) TRUE?

Show that the function f(x) = |sinx+cosx| is continuous at x = pi .

Show that the function f(x)=|sinx+cosx| is continuous at x = pi .

Show that the function f(x) = |sinx+cosx| is continuous at x = pi .