Problem 1E Problem 2E Problem 3E: (a) Sketch the plane curve with the given vector equation. (b) Find r'(t). (c) Sketch the position... Problem 4E Problem 5E: (a) Sketch the plane curve with the given vector equation. (b) Find r'(t). (c) Sketch the position... Problem 6E: (a) Sketch the plane curve with the given vector equation. (b) Find r'(t). (c) Sketch the position... Problem 7E Problem 8E Problem 9E: Find the derivative of the vector function. 9. t-2, 3, 1/t2 Problem 10E Problem 11E: Find the derivative of the vector function. 11. r(t) = t2i + cos(t2)j + sin2t k Problem 12E Problem 13E Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E Problem 21E: If r(t) = t, t2, t3, find r'(t), T( 1), r"(t). and r'(t) r"(t). Problem 22E: If r(t) = e2t, e2t, te2t, find T(0), r"(0), and r'(t) r"(t). Problem 23E Problem 24E Problem 25E Problem 26E: Find parametric equations for the tangent line to the curve with the given parametric equations at... Problem 27E: Find a vector equation for the tangent line to the curve of intersection of the cylinders x2 + y2 =... Problem 28E: Find the point on the curve r(t) = 2 cos t, 2 sin t, et, 0 t , where the tangent line is parallel... Problem 29E: Find parametric equations tor the tangent line to the curve with the given parametric equations at... Problem 30E: Find parametric equations tor the tangent line to the curve with the given parametric equations at... Problem 31E: Find parametric equations tor the tangent line to the curve with the given parametric equations at... Problem 32E: (a) Find the point of intersection of the tangent lines to the curve r(t) = sin t, 2 sin t, cos t)... Problem 33E Problem 34E: At what point do the curves r1(t) = t, 1 t, 3 + t2 and r2(s) = 3 s, s 2, s2 intersect? Find their... Problem 35E: Evaluate the integral. 35. 02(ti-t3j+3t5k)dt Problem 36E: Evaluate the integral. 36. 14(2t3/2i+(t+1)tk)dt Problem 37E: Evaluate the integral. 37. 01(1t+1i+1t2+1j+tt2+1k)dt Problem 38E: Evaluate the integral. 38. 0/4(secttanti+tcos2tj+sin22tcos2tk)dt Problem 39E: Evaluate the integral. 39. (sec2ti+t(t2+1)3j+t2lntk)dt Problem 40E: Evaluate the integral. 40. (te2ti+t1-tj+11-t2k)dt Problem 41E: Find r(t) if r'(t) = 2t i + 3t2 j + t k and r(1) = i + j. Problem 42E: Find r(t) if r'(t) = t i + et j + tet k and r(0) = i + j + k. Problem 43E: Prove Formula 1 of Theorem 3. Problem 44E: Prove Formula 3 of Theorem 3. Problem 45E Problem 46E Problem 47E: If u(t) = sin t, cos t, t) and v(t) = t, cos t, sin t, use Formula 4 of Theorem 3 to find... Problem 48E Problem 49E Problem 50E Problem 51E Problem 52E Problem 53E: Show that if r is a vector function such that r'' exists, then ddt[r(t)r(t)]=r(t)r''(t)] Problem 54E Problem 55E Problem 56E Problem 57E Problem 58E format_list_bulleted