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Knowledge: (25 marks) Application: (15 marks) 1) Differentiate each of the following. Do NOT simplify. 2) Determine the absolute maximum and minimum points for the function f (x) = -sinx + xcosx a) y = 2sin(3x) + cos(4x) in the interval[-7, 7]. b) y = cos' (5x2 ) .) f(x) = 4-sin(7x) 3) Find an equation of the tangent line to the curve y = 4sinxcos(2x) at x = 5" d) y = sin 5x + sec(3x) 4) A large pendulum is hung from the ceiling of a room. The position of its bob relative to the front of the room is given by x = 5 + 1.7cos(0.8nt), where xis measured in meters, and tis time, in seconds. ) Determine the period of the pendulum. e) f(x) = 6x-tan(x2 -1)]8 b) Determine the maximum and minimum distances of the pendulum bob from the front of the room. 3 csc(2x) f) 8(x) = 4- sin(5x) c) Determine the maximum and minimum speeds achieved by the pendulum bob and times that they occur. State the general case at which the times occur. (NEED to change this question) 8) y = sin3 1-Vx (1+Vx) Thinking, Inquiry, Problem Solving: (8 marks) 5) Ify = sin (x), show that Any + y' = 2x2. h) y = tan(cos(2x*)) y = xx tan(37x ) 6) Determine the x value(s) of the points of inflection for y = sinx in the interval [0,27]