If `f(x)=f(x)={(sin(a+1)x+sinx)/(x), ,x<0,c \ at x=0, (sqrt(x+b x^2)-sqrt(x))/(b xsqrt(x)),xgeq0,f(x)` is continuous at `x=0,t h e n` (a).`a=-3/2,b=0,c=1/2` (b) `a=-3/2,b=1,c=-1/2` (c)`a=-3/2,b in R-[0],c=1/2` (d) none of these

Determine the values of a , b , c for which the function f(x)={((sin(a+1)x+sinx)/(x ) ,, x 0):} is continuous at x=0

Determine the values of a ,\ b ,\ c for which the function f(x)={(sin(a+1)x+sinx)/x , for x 0 is continuous at x=0

If f(x)=(4+sin2x+a sinx+Bcosx)/(x^(2)) for x!=0 is continuous at x=0 , then A+B+f(0) is

{:("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"):}

Separate the intervals of concavity of the following functions (i) f(x)= sin^(-1)x ,(ii) f(x)=x+sinx

Find the range of the function " " f(x)=(sin^(2)x+sinx-1)/(sin^(2)x-sinx+2) .

If f(x)= =|{:(sinx+sin2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,sinx,1):}| then the value of int_(0)^(pi//2) f(x)dx , is

If f(x)=(sin^2 x+4sinx+5)/(2sin^2x+8sinx+8) then range of f(x) is

If f(x)= sin^(-1)x and g(x)=[sin(cosx)]+[cos(sinx)], then range of f(g(x)) is (where [*] denotes greatest integer function)

The period of f(x)=(1)/(2){(| sinx|)/(cos x)+(|cosx|)/(sinx)} , is