Calculus and Vectors Final Examination Find each limit if it exists. (3 marks each, A) 1 1 . 3 . 2 33 28 3 . \" a) 11m : 19) 11111 $ 0) 11m x)3 x x6 x>1 x+1 x>5 xS Sketch a graph ofthe function (x+2)2+ 1, x5 2 x + 1, 2 3. x 3 Is the function discontinuous? If yes, what is the type of each discontinuity? (2/2 marks, K/C) Differentiate. (2 marks each, K) (1)31 : (2x2 + 3)3(x 4)5 3x b)y:x2+5 4 C)y= ::S d) y : e4x192x e)y : sinch3 -cos3x Find the equation of the tangent to the curve y = (6x2 5x)(3x'2 x + 1)2 at the point where x : 1. Show all steps. (4/2 marks, A/C) Given the function y: 2363 15x2+36x23. 5.1. Determine its domain, range, x- and y-intercepts. (4 marks, A) 5.2. Determine critical numbers, local maxima and minima, and the intervals where the function is increasing and where it is decreasing. Explain your solution. (4/4 marks, A/C) 5.3. Determine points of inflection, and where the graph is concave up and where it is concave down. (4 marks, A) 5.4. Sketch a graph of the function. (2 marks, C) . The percent concentration of a certain drug in the bloodstream t hours after the drug was administered is given by the equation PU\") : 0.312/(1:2 + 4) where O S t S 5. Determine the maximum percent concentration and the time at which it occurs. (4 marks, A)