Spring 2007 - Linshaw's Class - Quiz 2 - Name TA Math 20C Quiz 2 Sec No PID Sec Time 1 Find parametric equations for the tangent line to the curve given

Spring 2007 - Linshaw's Class - Quiz 2 - Name TA Math 20C...

This preview shows page 1 out of 1 page.

Name:PID: 1. Find parametric equations for the tangent line to the curve given by r ( t ) = t 5 i + t 4 j + t 3 k , at the point (1 , 1 , 1). Solution: Note that r (1) = (1 , 1 , 1). We have r ( t ) = 5 t 4 i + 4 t 3 j + 3 t 2 k , so r (1) = 5 i + 4 j + 3 k . The tangent line passes through (1 , 1 , 1) and is parallel to the vector 5 i + 4 j + 3 k . We can parametrize this line as follows: x = 1 + 5 t, y = 1 + 4 t, x = 1 + 3 t. 2. Find the position function r ( t ) of a particle whose acceleration is a ( t ) = t i + t 2 j + cos 2 t k , which satisfies the initial conditions v (0) = i + k , and r (0) = j . Solution: Integrating a ( t ) yields v ( t ) = t 2 2 i + t 3 3 j + 1 2 sin 2 t k + C 1 , where

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture