If `a lt b` then f(x) =sqrt ((x-a)/(b-x))` is continuous on

If a lt b " then f(x) " f(x) = sqrt((x -a)/(b-x)) is continuous on

f(x)= [x] + sqrt(x -[x]) , where [.] is a greatest integer function then …….. (a) f(x) is continuous in R+ (b) f(x) is continuous in R (C) f(x) is continuous in R - 1 (d) None of these

f(x) is continuous on [a.b] then Statemant- I : underset(x to a^(+)) (Lt) f(x) = f(a) Statement-II : f is continuous for every x in (a,b) Statement-III underset (x to b^(-))(Lt) f(x) = f(b) Which of the following is true

If a twice differentiable function f(x) on (a,b) and continuous on [a, b] is such that f''(x)lt0 for all x in (a,b) then for any c in (a,b),(f(c)-f(a))/(f(b)-f(c))gt

Let f(x) be a function such that its derovative f'(x) is continuous in [a, b] and differentiable in (a, b). Consider a function phi(x)=f(b)-f(x)-(b-x)f'(x)-(b-x)^(2) A. If Rolle's theorem is applicable to phi(x) on, [a,b], answer following questions. If there exists some unmber c(a lt c lt b) such that phi'(c)=0 and f(b)=f(a)+(b-a)f'(a)+lambda(b-a)^(2)f''(c) , then lambda is

Let y = f(x) be defined in [a, b], then (i) Test of continuity at x = c, a lt c lt b (ii) Test of continuity at x = a (iii) Test of continuity at x = b Case I Test of continuity at x = c, a lt c lt b If y = f(x) be defined at x = c and its value f(c) be equal to limit of f(x) as x rarr c i.e. f(c) = lim_(x rarr c) f(x) or lim_(x rarr c^(-))f(x) = f(c) = lim_(x rarr c^(+)) f(x) or LHL = f(c) = RHL then, y = f(x) is continuous at x = c. Case II Test of continuity at x = a If RHL = f(a) Then, f(x) is said to be continuous at the end point x = a Case III Test of continuity at x = b, if LHL = f(b) Then, f(x) is continuous at right end x = b. If f(x) = {{:(sin x",",x le 0),(tan x",",0 lt x lt 2pi),(cos x",",2pi le x lt 3pi),(3pi",",x = 3pi):} , then f(x) is discontinuous at

Let y = f(x) be defined in [a, b], then (i) Test of continuity at x = c, a lt c lt b (ii) Test of continuity at x = a (iii) Test of continuity at x = b Case I Test of continuity at x = c, a lt c lt b If y = f(x) be defined at x = c and its value f(c) be equal to limit of f(x) as x rarr c i.e. f(c) = lim_(x rarr c) f(x) or lim_(x rarr c^(-))f(x) = f(c) = lim_(x rarr c^(+)) f(x) or LHL = f(c) = RHL then, y = f(x) is continuous at x = c. Case II Test of continuity at x = a If RHL = f(a) Then, f(x) is said to be continuous at the end point x = a Case III Test of continuity at x = b, if LHL = f(b) Then, f(x) is continuous at right end x = b. If f(x) = {{:(sin x",",x le 0),(tan x",",0 lt x lt 2pi),(cos x",",2pi le x lt 3pi),(3pi",",x = 3pi):} , then f(x) is discontinuous at