Vector Calculus Problems- PLEASE ANSWER ALL

Show transcribed image text 4. Let cl() = e(2n + 2 sin tj + t7k and C2 (t) = e-2'i + 6cosd-2t7k. (Use symbolic notation and fractions where needed.) dt 5. Find the velocity and acceleration vectors, the equation of the tangent line and the speed for the path c() = (4e (4), sin (7t), cos (70) at t = 0 (Use symbolic notation and fractions where needed. For the first three parts, give your answer in the form ( Velocity vector: v(0) Acceleration vector: a (0) = Equation of the tangent line (Use t for the parameter that takes all real values.) 1(1) = The speed (give your answer as an exact expression, i.e. do not give a decimal approximation), (0) = □. 1.
4. Let cl() = e(2n + 2 sin tj + t7k and C2 (t) = e-2'i + 6cosd-2t7k. (Use symbolic notation and fractions where needed.) dt 5. Find the velocity and acceleration vectors, the equation of the tangent line and the speed for the path c() = (4e (4), sin (7t), cos (70) at t = 0 (Use symbolic notation and fractions where needed. For the first three parts, give your answer in the form ( Velocity vector: v(0) Acceleration vector: a (0) = Equation of the tangent line (Use t for the parameter that takes all real values.) 1(1) = The speed (give your answer as an exact expression, i.e. do not give a decimal approximation), (0) = □. 1.





