Let : `f(x)={(a+3cosx)/(x^2),x<0btan(pi/([x+3])),xgeq0` If `f(x)` is continuous at `x=0,` then find `aa n db` , where `[dot]` denotes the greatest integer function.

Let f(x)=(e^(x))/(1+x^(2)) and g(x)=f'(x) , then

Let f(x)=lim_(ntooo) (x)/(x^(2n)+1). Then

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

Statement 1: Let f(x)=sin(cos x)in[0,pi/2]dot Then f(x) is decreasing in [0,pi/2] Statement 2: cosx is a decreasing function AAx in [0,pi/2]

Let f(x)=(x^(2)+2)/([x]),1 le x le3 , where [.] is the greatest integer function. Then the least value of f(x) is

Let f(x)=a bsinx+bsqrt(1-a^2)cosx+c , where |a| >0 then (a) c-b,c+b (b) difference of maximum and minimum values of f(x) is 2b (c) f(x)=c if x= -cos^(-1)a (d) f(x)=c if x= cos^(-1)a

Let f(x)=cospix+10x+3x^2+x^3,-2lt=xlt=3. The absolute minimum value of f(x) is 0 (b) -15 (c) 3-2pi none of these

Find f'(x) , given f(x)=(cosx)/(1+sinx)

Let f(x)={{:((x+1)^(3),-2ltxle-1),(x^(2//3)-1,-1ltxle1),(-(x-1)^(2),1ltxlt2):} . The total number of maxima and minima of f(x) is