Math1C - 1 QUIZ#1 ­ SOLUTIONS x = e− t t Sketch the...

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Unformatted text preview: 1) QUIZ #1 ­ SOLUTIONS x = e− t + t , Sketch the curve y = et − t , − 2 ≤ t ≤ 2 Indicate the direction as t increases. t = −2 ⇒ x = e2 − 2 ≈ 5.4, y = e−2 + 2 ≈ 2.1 t = 0 ⇒ x = 1, y = 1 t = 2 ⇒ x = e−2 + 2 ≈ 2.1, y = e2 − 2 ≈ 5.4 Direction is from t = −2 to t = 0 to t = 2, i.e. from ( 5.4, 2.1) to (1, 1) to ( 2.1, 5.4 ) . 2) Setup the integral to compute the length of the following curve. x = ln t , y = t + 1, 1 ≤ t ≤ 5 Simplify the integrand but do not attempt to solve the integral. dx 1 =, dt t dy 1 = dt 2 t + 1 1 1 t 2 + 4t + 4 ⎛ dx ⎞ ⎛ dy ⎞ = ⇒ ⎜ ⎟ +⎜ ⎟ = 2 + ⎝ dt ⎠ ⎝ dt ⎠ t 4 ( t + 1) 4 t 2 ( t + 1) 2 5 L= ∫ 1 2 t 2 + 4t + 4 dt = 4 t 2 ( t + 1) t+2 ∫ 2t t + 1 dt 1 5 ( t + 2 )2 ∫ ( 2t )2 (t + 1) dt = 1 5 ...
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This note was uploaded on 09/06/2011 for the course MATH 1c taught by Professor Garrison during the Spring '11 term at DeAnza College.

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