If [t] denotes the greatest integer ≤t, then the number of points, at which the function f(x)=4∣2x+3∣+9[x+21]−12[x+20] is not differentiable in the open interval (−20,20), is ________.
Let a function f:R→R be defined as :
f(x)={∫0x(5−∣t−3∣)dt,x2+bx,x>4x≤4
where b∈R. If f is continuous at x=4, then which of the following statements is NOT true?
Let f:R→R be a differentiable function such that f(4π)=2, f(2π)=0 and f′(2π)=1 and
let g(x)=∫xπ/4(f′(t)sect+tantsectf(t))dt for x∈[4π,2π). Then limx→(2π)−g(x) is equal to :
Let f:R→R be a continuous function satisfying f(x)+f(x+k)=n, for all x∈R where k>0 and n is a positive integer. If I1=∫04nkf(x)dx and I2=∫−k3kf(x)dx, then :
Let [t] denote the greatest integer ≤t and {t} denote the fractional part of t. The integral value of α for which the left hand limit of the function
f(x)=[1+x]+2[x]+{x}α2[x]+{x}+[x]−1 at x=0 is equal to α−34, is ________.
Let f(x)=min{1,1+xsinx}, 0≤x≤2π. If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to
Let x=2t, y=3t2 be a conic. Let S be the focus and B be the point on the axis of the conic such that SA⊥BA, where A is any point on the conic. If k is the ordinate of the centroid of the ΔSAB, then t→1limk is equal to :
