hw5 - F ( t ) = ( e t , sin t ) at the point (1 , 0). 6....

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MATH 138: Calculus 2 Assignment #5 Due: 12:30 p.m., Friday, October 29 Fall 2010 1. Find a Cartesian equation (i.e., x - y equation) of the curve by eliminating the parameter, and then sketch the curve. (a) x = e t - 1 , y = e 2 t , -∞ < t < . (b) x = ln t, y = t, t 1. (c) x = 1 + t, y = 5 - 2 t, t R . 2. Find parametric equations for the ellipse x 2 a 2 + y 2 b 2 = 1 where a > 0 and b > 0. You must specify the range of parameter. 3. Set up an integral that represents the arc-length of the curve. You don’t need to compute the integral. (a) x = 1 + e t , y = t 2 , - 3 t 3. (b) x = ln t, y = t + 1 , 1 t 5. 4. Find the arc-length of the curve. You must evaluate the integral. (a) x = e t + e - t , y = 5 - 2 t, 0 t 3. (b) x = cos(2 t ) , y = sin(2 t ) , 0 t π . 5. Find the tangent line to the curve
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Unformatted text preview: F ( t ) = ( e t , sin t ) at the point (1 , 0). 6. Find the tangent line to the curve F ( t ) = (cos t,t ) at the parameter value t = . 7. A certain bacterial culture undergoing exponential growth doubles in size after 5 sec-onds. If the culture contains 100 specimens at time t = 0, when will the number have increased to 2000 specimens? The following problems are only recommended, not for submission. Stewart: Section 10.1 Exercises 5, 11, 15; Section 10.2 Exercises 3, 5, 9, 37, 45; Exam-ples 15 in Section 10.1 and Examples 4 and 5 in Section 10.2....
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