At 5 an 1 f none of these 5 find the length of the

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Unformatted text preview: . a. aT = 2, aN = 1 b. aT = 1, aN = 2 c. aT = 1, aN = −2 d. aT = 1, aN = 5 e. aT = 5, aN = 1 f. None of these. 5. Find the length of the curve given by r (t ) = ti + ln(sec t ) j + 3k from t = 0 to t = ( 2) ln (1 + 2 ) ln ( 2 − 1) π 4 a. ln b. c. d. ln ( 2 ) e. None of these. 6. Find the length of the curve given by r (t ) = ( t sin t + cos t ) i + ( sin t − t cos t ) j + t = 0 to t = 2π a. 2π 2 b. 2π c. 4π 2 d. 4π e. None of these. 7. Find the curvature of y = e− x 1 a. 3/2 1 + e−2 x ( b. c. d. ) e− x (1 + e ) −2 x 3/ 2 e− x (1 + e ) − x 3/2 (e e− x −x + e −2 x ) 3/2 e. None of these. 32 t k from 2 8. ⎛ 4⎞ Find the radius of curvature for 6 y = x3 at the point ⎜ 2, ⎟ ⎝ 3⎠ a. 5...
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