A particle moves along the x-axis so that its velocity at time t, 0 < t < 5, is given by v(t) = 3(t - 1)(t - 3). At time 2, the position of the particle is x(2) = 0. a) Find the minimum acceleration of the particle. b) Find the total distance traveled by the particle. c) Find the average velocity of the particle over the interval 0 < t < 5.
The function f is defined by f(x) = √(25 - x^2) for -5 < x < 5. a) Find f'(x). b) Write an equation for the line tangent to the graph of f at x = -3 for -5 < x < -3.
Let g be the function defined by g(x) = {0, for -3 < x < 5. Is g continuous at x = -3? Use the definition of continuity to explain your answer. Find the value of ∫(√(5 - x^2)) dx.