Question 1 [30 points] a) [10 points] Given the vector function r(t) = (t² − 1, e¯5t, sin(–2t)), find the unit tangent v

[answerhappygod]

Question 1 30 Points A 10 Points Given The Vector Function R T T 1 E 5t Sin 2t Find The Unit Tangent V 1 (65.12 KiB) Viewed 14 times

Question 1 [30 points] a) [10 points] Given the vector function r(t) = (t² − 1, e¯5t, sin(–2t)), find the unit tangent vector at the point - (-1,1,0). Evaluate the integral [ r(t) dt. b) [8 points] Find the possible points on the vector function r(t) = (t³,3t,tª) for which the normal plane is parallel to the plane 6x + 6y - 8z = 1. Find the normal plane equation. c) [12 points] For the function √16-x²-y² f(x, y) = cos(-)√√9-2² sketch it. Provide your detail solution. find the domain and