mat135_test2_verA (2).pdf

Leave blank if always concave down f f is concave

• Test Prep
• 15

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Leave blank if always concave down.) (f) f is concave down on . (Use interval notation. Leave blank if always concave up.) (g) f has inflection point(s) at x = . (Leave blank if there are none.) (h) f has horizontal asymptotes y = . (Leave blank if there are none.) (i) f has vertical asymptotes at x = . (Leave blank if there are none.) (j) f is EVEN, ODD, NEITHER. (Circle the correct answer.) 9 Continues on the next page

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VER A MAT 135Y - Term Test 2 - Fall/Winter 2017-2018 Page 10 of 15 PART III (Long Answer): Please answer the following questions. You should provide complete solutions, and show your work. Part marks are available, when warranted. Correct final answers with little or no work will not receive any credit. (1) (a) Find lim x →∞ xe - x 2 . Distinguish between ±∞ and does not exist (DNE), where ap- propriate. So lim x →∞ xe - x 2 = . (b) Compute lim x 0 + (1 + x ) 7 cot x . Distinguish between ±∞ and does not exist (DNE), where appropriate. So lim x 0 + (1 + x ) 7 cot x = . 10 Continues on the next page
VER A MAT 135Y - Term Test 2 - Fall/Winter 2017-2018 Page 11 of 15 (c) Find the equation of the tangent line to the curve x 2 y 3 + cos( xy ) = e x + y at the point (0 , 0). So the equation of the tangent line is: . 11 Continues on the next page

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VER A MAT 135Y - Term Test 2 - Fall/Winter 2017-2018 Page 12 of 15 (2) Atmospheric pressure decreases with altitude, and satisfies an exponential decay model P = Ae kx , where P is pressure (in kPa) and x is altitude (in metres). The pressure at sea level (where altitude is 0) is about 100 kPa. (a) If pressure decreases by 12% for every 1000 metres increase in altitude, find the values of A and k in the equation P = Ae kx . (You should leave your values for A and k in exact form. Do not simplify.) So A = , and k = . (b) At what altitude is the pressure 75 kPa? (You should leave your final answer in exact form. Do not simplify.) So the pressure will be 75 kPa at an altitude of x = . 12 Continues on the next page
VER A MAT 135Y - Term Test 2 - Fall/Winter 2017-2018 Page 13 of 15 (3) Water drains from a conical tank at the rate of 5 ft 3 / min. The height of the tank is 10 ft and the radius at the top of the tank is 4 ft. How fast is the water level dropping when the water level is 6ft?

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• Fall '13
• Derivative, Convex function, Concave function, David Belanger

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