Find parametric equations for the tangent line

Chapter 10, Problem 40

(choose chapter or problem)

Find parametric equations for the tangent line to the curve , , at the point . Graph the curve and the tangent line on a common screen. 22 x y ) d t 0 sin(1 22 ) d rt t i 2t j t 2 k 45 at 6t i 12t 2 i j 3k j 6t k rt t ln t i t j et k y x 4 x 2 y x 1, 1 4 3, 0 0, 4 x 3 cos t y 4 sin t rt 1 3 t 3 , 1 2 t 2 , t t 1, 0, 1 rt et i et sin t j et cos t k r2t 1 ti t 1, 0, 0 2 j t 3 k r1t cos t i sin t j t k 0 t 1 rt 2t 32 , cos 2t, sin 2t 0 t 3 z t 4 y t 3 x t 2 n 6 C 1, 1, 0 1, 1, 0 z ln t C xz x 2 t y 2t 1 3 C x 1 0 rt t rt dt 2 i t cost j sint k 23. Determine whether the lines give