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MATH 161 - EXAM I NAME ____________________ DO NOT SIMPLIFY YOUR ANSWERS 1. (5 points each) Find each of the following limits (if it exists): a) lim 2x + 1 b) lim x 2 x 3 x1 c) lim x ∞ x2 + 9 x2 x 6 2x3 + 9_ 4 x3 + 3 d) Let 2. (10 points) For the equation f (x) = 4x2 x find the equation of the tangent line at x = 1 3. (10 points) Use the limit definition of the derivative to find the derivative of 4. (10 points each) Differentiate each of the following: a) +5 b) c) d) 5. (10 points) Use implicit differentiation to find dy/dx when x3 y + y2 – 5x2 = 4 6. (10 points) A cylindrical tank stock has a height of 6 feet and its radius of 4. Water is being pumped into the tank. The height of the water in the tank is rising at a rate of 2 feet per hour. How fast is the volume of the tank increasing? (Hint: V=πr2h)