[" (ii) "f(x)=3+(x-5)],[" (iii) "f(x)=tan x" on "[0,pi]]

Discuss the applicability of Rolles theorem for f(x)=tan x on [0,pi]

Let f(x)=(1-tan x)/(4x-pi),x!=(pi)/(4),x in[0,(pi)/(2)], If f(x) is continuous in [0,(pi)/(4)], then find the value of f((pi)/(4))

Let f(x)=(1-tan x)/(4x-pi), x ne pi/4, x in [0,pi/2]." If f(x) is continuous in "[0,pi/4]," then "f(pi/4)is

the function f(x)=(6/5)^((tan6x)/(tan5x)) if x is 0 to pi/2 and f(x)=b+2 if x=pi/2 and f(x)=(1+|cosx|)^{(a*|tanx|)/b} if x is pi/2 to pi Determine the values of a&b. if f is continuous at x=pi/2

if f(x) = {:{ (1+x, ,0 le x le2), (3-x, ,2 lt x le3):} Determine the points of discontinuity of the function f (f(x)) (ii) Check the continuity of the function f(x) = [x]^(2) - [x^(2)] (iii) find the values of a and b if f is continuous at x = pi/2 f(x)= {:{((8/5)""^(tan8x)/(tan 5x) , , 0 lt x lt pi//2),(a+4, , x=pi//2), ((1+|cot x|)""^(b|tan x|)/a, , pi/2 lt x lt pi):}

If f(x)=3^(-x)-1 , for -1 le x lt0, =tan(x//2), " for "0lexltpi =(x)/(x^(2)-2)," for "pilexlt6, then f(-1)+f(pi//6)+f(5)=

Show that (i) int_(0)^(pi//2)f(sinx) d x=int_(0)^(pi//2)f(cos x) d x (ii) int_(0)^(pi//2)f(tan x) d x=int_(0)^(pi//2)f(cot x) d x (iii) int_(0)^(pi//2)f(sin 2 x) sin xd x = int_(o)^(pi//2)f(sin 2x).cosx d x

Show that (i) int_(0)^(pi//2)f(sinx) d x=int_(0)^(pi//2)f(cos x) d x (ii) int_(0)^(pi//2)f(tan x) d x=int_(0)^(pi//2)f(cot x) d x (iii) int_(0)^(pi//2)f(sin 2 x) sin xd x = int_(o)^(pi//2)f(sin 2x).cosx d x