Calculus Continuity Mock Tests

Let f(x) = |x - 1| + |x - 2| + |x - 3| for x in R. Which of the following is/are TRUE?

Let f(x) = { (sin(ax) + sin(bx))/x for x ≠ 0, a + b for x = 0 }. If f is continuous at x = 0, then:

Let f(x) = |x^2 - 1| + |x^2 - 4| for x in R. The number of points where f is not differentiable is

Let f(x) = { x^n · sin(1/x) if x ≠ 0; 0 if x = 0 }, where n is a positive integer. Which of the following statements is/are TRUE?

The number of points where the function f(x) = |x - 1| + |x - 2| is not differentiable is:

Let f(x) = max{x, x³} for x ∈ ℝ. The set of points where f is not differentiable is:

The value of lim(x→0) (sin(x) - x) / x³ equals: