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EM 122 ME SP 2ND SEM AY 2014 - 2015 - College of...

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Unformatted text preview: College of Engineering University of San Carlos Nasipit, Talamban, Cebu City 6000 Philippines College Midterm Examinations on Engineering Mathematics Course: EM 122 Calculus 1 Approved by: Exam Schedule: February 7, 2015; 9:00 a.m.-12.‘00 Noon. Exam Engr. Ricardo L. Forms; and Engr. Dr. Evelyn B. Taboada Committee: Patrick U. Tan College Dean QUESTIONNAIRE General Instruction: Do as directed in Tests 1, 2 & 3. Present in writing the full details of your answers or solutions in the bluebook provided The grades you earn for each item will be based on correctness comgleteness, and clarity of gresentation. Test 1. Answer the following problems as specified. Time Allocation: 45 minutes Weight: 30% 1) 2) 3) 4) 5) 6) 7) Given f(x): 3x+2 if x<4 5x+k if 43x Find the value of k such that lim f (x) exists. x—>4 Find the point of inflection of the curve slope of the tangent to the curve y = x3 — x2 — x Ify=x2 3x2+2 find Q dx A cell is spherical in shape. Find the rate of change of the volume of the cell with respect to the diameter when the diameter is 3 micrometer. At what point on the curve y = 2x2 — 4x — 1 would the slope of the tangent line be 4? x + 2 Find ’ of = . y y x2 _ 3 . 2 2 — 7 + 6 Evaluate the limit :llmH2 [x—:] x _ 8) Given that f(x)=\/2x+x2 and g(x)=x2—16,find (gof)(x) Test 2. Answer the following problems as specified. Time Allocation: 75 minutes Weight: 50% 1) 2) 3) 4) 5) 6) 7) dzy 2 Given x2 + 25 y2 = 100, find when x=8. Find the maximum possible area of a rectangle whose two vertices are on the x-axis and the other two vertices are on the curve )62 + y — 9 = 0 . Water runs into an inverted conical tank at the rate of 8m3/hr. If the height of the tank is 6m and the base diameter is 4m, how fast is the water level rising when the water is 3m deep? Two lines through the point (—1,3) are tangent to the curve x2 + 4 y2 — 4x — 8y + 3 = 0. Find the equation of each line. Find the area of the largest rectangle that can be placed inside the triangle ABC whose sides are AB=3m, BC=4m, and AC=5m if one side of the rectangle is on side AC of the triangle. If f (x) = ax3 + bx2 + cx, determine a, b, and c so that the graph will have a point of inflection at (1,2) and so that the slope of the inflectional tangent there will be -2. A cardboard box manufacturer wishes to make open boxes from pieces of cardboard 12 inches square by cutting equal squares from the four corners and turning up the sides. Find the length of the side of the square to be cut out in order to obtain a box of the largest possible volume. Test 3. Answer the following problems as specified. Time Allocation: 30 minutes Weight: 20% 1) 2) Find the radius and height of the right-circular cylinder of largest volume that can be inscribed in a sphere of radius 200m. Tuition at small college is currently Php8,000 per semester. The college currently has 1000 students. If tuition is increasing at the rate of Php400 per semester and enrolment is declining at the rate of 20 students per year, find the rate at which semestral revenues from tuition will be changing two years from now? ...
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