13-2 - Solutions to Homework Assignment 9 5 Notice that y =...

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Unformatted text preview: Solutions to Homework Assignment 9 5. Notice that y = ( x- 1) 2 , so this is the parabola y = x 2 shifted right 1 unit. r prime ( t ) = < 1 , 2 t > . At t = 1 , this is < 1 , 2 > . The graphs are below. The position vector is blue and the tangent vector is green. 6. Here, y = 1 /x and neither x nor y can be negative or zero. We just get the arm of the hyperbola in the first quadrant. r prime ( t ) = < e t ,- e- t > . At t = 0 , this is < 1 ,- 1 > .-2-4-2-4 4 4 2 2-2-4-2-4 4 4 2 2 Number 5 Number 6 10. r prime ( t ) = <- 3 sin(3 t ) , 1 , 3 cos(3 t ) > . 13. r prime ( t ) = (bigg 2 te t 2 , , 3 1 + 3 t )bigg . 15. r prime ( t ) = vector b + 2 tvector c. 21. r prime ( t ) = < 1 , 2 t, 3 t 2 >, so T ( t ) = < 1 , 2 t, 3 t 2 > √ 1 + 4 t 2 + 9 t 4 . Thus, T (1) = 1 , 2 , 3 √ 14 . r primeprime ( t ) = < , 2 , 6 t > . r prime ( t ) × r primeprime ( t ) = < 1 , 2 t, 3 t 2 > × < , 2 , 6 t > = < 12 t 2- 6 t 2 ,- (6 t- 0) , 2- > = < 6 t 2 ,- 6 t, 2 > ....
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