Unformatted text preview: WORKSHEET 18  Fall 1995 1. a) For each of the following equations, find dy dx : i) x 2 + y 2 = 1 ii) y = cot 2 x iii) y 2 sin x = x 3 + 5 x 2 4 b) For each equation above, find dx dy . Explain the difference between the meaning of this derivative and the one you found in part a). c) Now suppose that x and y are both dependent on the variable t (perhaps t denotes time). For each equation above, suppose also that these functions x ( t ) and y ( t ) satisfy the equation for all times t . Differentiate each expression with respect to t . Solve for both dx dt and dy dt . Explain the meanings of these derivatives. 2. Suppose a particle is moving along a circle described by the equation x 2 + y 2 = 1 as in part a) of the previous problem. Here the unit length is one meter, and time t is measured in seconds. a) Which derivative expresses the rate (in m/s) at which x is changing? b) Which derivative expresses the rate (in m/s) at which y is changing?...
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 Spring '08
 Grether
 Equations, Derivative, Vector Space, curve x2

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