210ExamReview2

# 210ExamReview2 - s P 3800 airplane 7 Assume that oil...

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Math 210 Fall 2007 Exam 2 Review 1) Find the derivative using the limit definition. You may not use any shortcuts. Proper notation is required. a) 1 2 ) ( 3 - + = x x x f b) 2 1 ) ( x x f = 2) Find the equation of the tangent line to the given curve at the given x-value a) 4 3 2 3 2 - + = x x y at x = 1 b) = x y 3 1 sec at x = 4 3 π 3) A particle moves on a line away from its initial position so that after t hours the particle has traveled a distance of t t d + = 2 3 in miles. a) Find the average velocity over the interval [1,3] b) Find the instantaneous velocity at t = 2 4) For the function 2 3 1 - + = x x y find 2 2 dx y d and evaluate it at x = 3 5) Find the equation of the line tangent to the curve 3 2 3 = + xy y at the point (1,1) 6) An airplane is flying on a horizontal path at a height of 3800 ft. as shown. At what rate is the distance s between the airplane and the fixed point P changing with respect to θ when 30 = θ ° Express the answer in units of ft/degree.

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Unformatted text preview: s P 3800 airplane! 7) Assume that oil spilled from a ruptured tanker spreads in a circular pattern whose radius increases at a constant rate of 2 ft/sec. How fast is the area of the spill increasing when the radius of the spill is 60 ft? 8) Make sure you know how to take derivatives of all the types of functions we talked about in class. This includes • Taking derivatives using the exponent rule • Taking derivatives using the product rule • Taking derivatives using the quotient rule • Taking derivatives using the chain rule • Taking derivatives of the trig functions • Taking derivatives of functions in which you have to use more than one of the above bulleted techniques. A good way to study these is to look at examples from class in your notes....
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