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Chu Instructions: QuestionMarks123456789101112131415No books or notes are permitted. Only calculators without text storage and graphical capability are permitted. Please show all your work clearly. Please justify all your answers. Please write P.T.O. if you write your answer at the back of the page. Unless otherwise stated, please correct your answers to four decimal places. This examination consists of 15 questions. This exam must be returned intact. [8 Marks] Find the limits: EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 [6 Marks] Using only the limit definition, find the derivative of EMBED Equation.DSMT4 . [9 Marks] Find the derivatives: EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.3 [5 Marks] If EMBED Equation.DSMT4 , find EMBED Equation.DSMT4 . [5 Marks] If EMBED Equation.3 , find the equation of the line tangent to this curve at x = 1. [4 Marks] Consider the function EMBED Equation.DSMT4 . Use Newton’s method to find an approximation to the root of this function by taking 2 iterations. Assume the initial point is x = 0.5. (Answer to 5 decimal points). [16 Marks] Find the respective anti-derivatives: EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.3 [5 Marks] Find the area of the region bounded by the curves whose equations are EMBED Equation.DSMT4 and EMBED Equation.DSMT4 . [6 Marks] Use the trapezoidal rule to approximate EMBED Equation.3 . Assume n = 4 or 4 division points. (Answer to 5 decimal points). [12 Marks] Consider the following function EMBED Equation.3 . Find the y-intercept. Find the x-intercept(s). Find the intervals of increase and decrease. Specify any local maximum or minimum value(s). Find the intervals of concavity. Specify any point(s) of infection. Sketch the curve. [4 Marks] Use differentials to find the approximate value of EMBED Equation.DSMT4 . [5 Marks] Sand is being dropped on a pile in the shape of a cone. How fast is the height increasing when the pile is 7 meters high? Assume height is always equal to the diameter and EMBED Equation.3 [5 Marks] A cardboard box is to be constructed from a 10 cm x 10 cm cardboard. The box is constructed by cutting out 4 square corners and folding up the sides. What dimensions will maximize the volume of the resulting box? [5 Marks] If the semi-circle whose equation is EMBED Equation.DSMT4 , is revolved about the x-axis, find the volume of the resulting solid using disc method. [5 Marks] If the region bounded by EMBED Equation.DSMT4 , EMBED Equation.DSMT4 , EMBED Equation.DSMT4 and EMBED Equation.3 is revolved about the y-axis, what is the volume of the resulting solid using shell method? 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