" $b."f(x)=[[x]-x]+|sin x|

Find the derivatives of the functions. (a) f(x) =x^8 (b) f(x) =x^3 + sin x f(x) =x^3 sin x

Let f (x) = |sin x| then f (x) is

If f(x)=2x+[x]+sin x cos x, Then f is:

f(x) = (x - [x]) sin ((1)/(X)) , at x = 0 , f is

f(x) = (x)/(sin x) is

Discuss the continuity of the following functions: (a) f(x) = sin x + cos x (b) f(x) = sin x - cos x (c) f(x) = sin x . cos x

{:("Column-I","Column-II"),(A.f(x) = (1)/(sqrt(x -2)),p.lim_(x to 0)f(x) =1),(B. f(x) = (3x - "sin"x)/(x + "sin" x), q. lim_(x to 0)f(x) = 0),(C.f(x) = x "sin"(pi)/(x) f(0)=0,r.lim_(x to oo) f(x) = 0),(f(x) = tan^(-1) (1)/(x),s.lim_(x to 0) "does not exist"):}

{:("Column-I","Column-II"),(A.f(x) = (1)/(sqrt(x -2)),p.lim_(x to 0)f(x) =1),(B. f(x) = (3x - "sin"x)/(x + "sin" x), q. lim_(x to 0)f(x) = 0),(C.f(x) = x "sin"(pi)/(x) f(0)=0,r.lim_(x to oo) f(x) = 0),(f(x) = tan^(-1) (1)/(x),s.lim_(x to 0) "does not exist"):}

In [0,1] Lagranges Mean Value theorem in NOT applicable to f(x)={(1)/(2)-x;x =(1)/(2) b.f(x)={(sin x)/(x),x!=01,x=0 c.f(x)=x|x| d.f(x)=|x|

In [0,1] Lagranges Mean Value theorem in NOT applicable to f(x)={1/2-x ; x =1/2 b. f(x)={(sin x)/x ,x!=0 1,x=0^ c. f(x)=x|x| d. f(x)=|x|