Calculus and Vectors MCV4U Graded Assignment 1 8. The points of inflections and the local maximum and minimum values of the function y = 2sinx + sin x in the domain of [0, 2x ] 16 (A, C) 9. The position x, of the midpoint of the vibrating violin string is described by the formula x = 0.05cos (880mt), where x is measured in centimeters and t is measured in seconds. a) Determine the formulas for the velocity and the acceleration of the midpoint of the string. b) Determine the maximum speed of the vibration of the string in centimeters per second. c) Show that the acceleration and position satisfy the differential equation, d x/dt+ (880n) x = 0 16 (A) 10. Show that if y = x/tan(x) then y *= cot(x) - xcsc(x) /6 (T/D) 11. A weight is oscillating up and down on spring. It's displacement from rest is given by the function d(t) = sin 6t - 4cos 61, where d is in centimetres and t is time in seconds. a) What is the rate of change of the displacement after 1 s? 16 (C/A) b) Determine the maximum and minimum displacements and when they first occur.Choose any 4 questions: (Handwritten answers will be accepted only) 6. Differentiate each given functions 19 (K/U) sec x a) y= cos2x b) y = Sin' (cos x + Tan x) c) y = 4xsin (6x2 -2) 7. Determine f "(x) 18 (K/U) a) f(x) = cot (4x) + csc (x) b) f(x) = sin (x) tan(x)