ws18 - WORKSHEET 18 Fall 1995 1 a For each of the following...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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?...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online