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

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

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

## 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.

Ask a homework question - tutors are online