`L e tf(x)={x^3+x^2+3x+sinx|(3+s in1/x ,),x!=0. 0x=0` then the number of point where `f(x)` attains its minimum value is_____

if f(x)={x^3 x<0 3a+x^2 x≥0 is continuous at x = 0 , then a is

If f(x) = (2x + 3 sin x)/( 3x + 2 sin x), x ne 0 is continuous at x = 0 , then find f(0)

f(x)=|a x-b|+c|x|AAx in (-oo,oo), where a >0, b >0,c > 0. Find the condition if f(x) attains the minimum value only at one point.

Find number of roots of f(x) where f(x) = 1/(x+1)^3 -3x + sin x

If L=lim_(x->0)(e^(-(x^2/2))-cosx)/(x^3 sinx), then the value of 1/(3L) is

Let f(x)={(1+3x)^(1/x), x != 0e^3,x=0 Discuss the continuity of f(x) at (a) x=0, (b) x=1

Given that f'(x)=4x^(3)-3x^(2)+2x-1 find f(x) if f(0)=0 .

f(x)={cos(pix)/2,x >0x+a ,xlt=0 Find the values of a if x=0 is a point of maxima.

L e tf(x)={x^2+3x ,-1lt=x<0-sinx ,0lt=x

L e tf(x)=x^3-(3x^2)/2+x+1/4 Then the value of (int_(1/4)^(3/4)f(f(x))dx)^(-1) is____