a= 12 b=1.2 c=0.1

Calculus

Differential Calculus In questions 1 to 5 you should use the values of a, b and c allocated to you in Table 1. 1) Differentiate a) y = 10e'\" + 16x b)y = bt3 + 6sin(2t) 7 2) Use the product rule to differentiate y = (3t2 + (06:5t 3) Find the velocity v = Z: of an object falling through the atmosphere 4) 5) at a height y of y = 2000 + 15:: 0.002t4 Give the velocity after t = :1 seconds Using the chain rule, calculate the derivative ST: of the function y = in (bx3 7) . d and so determine the value of 3:1 when x = 2. A cantilevered beam is subjected to a complex periodic wind loading and experiences a vibration at its unsupported end of x = 0.63 + csin(3t) 0.25 cos(5t) metres dx Find an expression for the velocity v = E of the unsupported end and give the value of the velocity when t = 0.3 seconds