MTH164FA10-M1d_ans

5t page 5 of 8 1st midterm exam mth 164 multivariable

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Unformatted text preview: Answer: Page 4 of 8 1st Midterm Exam MTH 164 (Multivariable Calculus) Tuesday, October 19, 2010 The chain rule in this case: dw ∂ w dx ∂ w dy ∂ w dz = + + dt ∂ x dt ∂ y dt ∂ z dt becomes dw 1 x 1 y = et + (− 2 + )(2 cos 2t) + (− 2 (−4 sin 4t) dt y y z z evaluating at t = 0 gives a value of 2 . 3 6. (10 points) Match the parametric equations with the graphs labeled I-V. x = t + sin(4t) (A) y = t + sin(3t) x = sin(t + sin(7t)) (C) y = cos(t) x = | cos(t)| · cos(t) (E) y = | sin(t)| · sin(t) x = sin(t) (B) y = cos(t) − 2 cos(2t) x = 6 cos(t) + cos(4.5t) (D) y = 6 sin(t) − sin(4.5t) Page 5 of 8 1st Midterm Exam MTH 164 (Multivariable Calculus) Tuesday, October 19, 2010 I II III IV V Answer: I:A, II:E, II...
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This document was uploaded on 05/06/2013.

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