uppose a function is not defined at 0, for example f (x) = 1x , what does this tell us about limx→0 f (x)?

Let f : [0, π] → R be defined byf (x) =(0 if x = 0,x sin 1x − 1x cos 1x if x̸ = 0.Is f continuous?

Suppose a function is not defined at 0, for example f (x) = 1x , what does this tell us about limx→0 f (x)

Let f:→R→(0,∞) be strictly increasing function such that limx→∞f(7x)f(x)=1. Then, the value of limx→∞[f(5x)f(x)−1] is equal to

Find k such that the function f defined byfX (x) =kx2, 0 < x < 1,0, otherwiseis a probability density function. Also, determine P (1/3 < X ≤ 1/2

Let f(x) be a real value function such that f(x)=2x−1x−2∀ x ∈ (2,∞) and g(x)=x2+1x+(f(x))2+1f(x)∀ x>2, then minimum value of g(x) is