Problem 1QC: Restrict the domain o f the vector function in Example 1 to produce a line segment that goes from... Problem 2QC: Explain why the curve in Example 5 lies on the cylinder x2+y2=1,as shown in Figure 14.7 Example 5... Problem 1E: How many independent variables does the function r(t) = f(t), g(t), h(t) have? Problem 2E: How many dependent scalar variables does the function r(t) = f(t), g(t), h(t) have? Problem 3E Problem 4E Problem 5E: How do you evaluate limtar(t), where r(t) = f(t), g(t), h(t)? Problem 6E: How do you determine whether r(t) = f(t) i + g(t) j + h(t) k is continuous at t = a? Problem 7E: Find a function r(t) for the line passing through the points P(0,0,0) and Q(1,2,3). Express your... Problem 8E: Find a function r(t) whose graph is a circle of radius 1 parallel to the xyplane and centered at... Problem 9E Problem 10E Problem 11E: Lines and line segments Find a function r(t) that describes the given line or line segment. 11. The... Problem 12E: 914. Lines and line segments Find a function r(t) that describes the given line or line segment. The... Problem 13E Problem 14E Problem 15E: Graphing curves Graph the curves described by the following functions, indicating the positive... Problem 16E: Graphing curves Graph the curves described by the following functions, indicating the positive... Problem 17E: Graphing curves Graph the curves described by the following functions, indicating the positive... Problem 18E: Graphing curves Graph the curves described by the following functions, indicating the positive... Problem 19E: Curves in space Graph the curves described by the following functions, indicating the positive... Problem 20E: Curves in space Graph the curves described by the following functions, indicating the positive... Problem 21E: Curves in space Graph the curves described by the following functions, indicating the positive... Problem 22E: Curves in space Graph the curves described by the following functions, indicating the positive... Problem 23E: Curves in space Graph the curves described by the following functions, indicating the positive... Problem 24E: Curves in space Graph the curves described by the following functions, indicating the positive... Problem 25E: Curves in space Graph the curves described by the following functions, indicating the positive... Problem 26E: Curves in space Graph the curves described by the following functions, indicating the positive... Problem 27E: Exotic curves Graph the curves described by the following functions. Use analysis to anticipate the... Problem 28E: Exotic curves Graph the curves described by the following functions. Use analysis to anticipate the... Problem 29E: Exotic curves Graph the curves described by the following functions. Use analysis to anticipate the... Problem 30E: Exotic curves Graph the curves described by the following functions. Use analysis to anticipate the... Problem 31E: Limits Evaluate the following limits. 41. limt/2(cos2ti4sintj+2tk) Problem 32E: Limits Evaluate the following limits. 42. limtln/2(2eti+6etj4e2tk) Problem 33E: Limits Evaluate the following limits. 43. limt(eti2tt+1j+tan1tk) Problem 34E: Limits Evaluate the following limits. 44. limt2(tt2+1i4etsintj+14t+1k) Problem 35E: Limits Evaluate the following limits. 45. limt0(sinttiett1tj+cost+t2/21t2k) Problem 36E: Limits Evaluate the following limits. 46. limt0(tantti3tsintj+t+1k) Problem 37E Problem 38E: Domains Find the domain of the following vector-valued functions. 56. r(t)=2t1i+3t+2j Problem 39E: Domains Find the domain of the following vector-valued functions. 57. r(t)=t+2i+2tj Problem 40E: Domains Find the domain of the following vector-valued functions. 58. r(t)=cos2ti+etj+12tk Problem 41E Problem 42E: Curve-plane intersections Find the points (if they exist) at which the following planes and curves... Problem 43E: Curve-plane intersections Find the points (if they exist) at which the following planes and curves... Problem 44E: Curve-plane intersections Find the points (if they exist) at which the following planes and curves... Problem 45E: Matching functions with graphs Match functions af with the appropriate graphs AF. a. r(t) = t, t, t... Problem 46E Problem 47E: 4750. Curve of intersection Find a function r(t) that describes the curve where the following... Problem 48E: 4750. Curve of intersection Find a function r(t) that describes the curve where the following... Problem 49E: 4750. Curve of intersection Find a function r(t) that describes the curve where the following... Problem 50E: Curve of intersection Find a function r(t) that describes the curve where the following surfaces... Problem 51E: Golf slice A golfer launches a tee shot down a horizontal fairway; it follows a path given by r(t) =... Problem 52E: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the... Problem 53E: 5256. Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the... Problem 54E: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the... Problem 55E: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the... Problem 56E: 5256. Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the... Problem 57E: 5758. Closest point on a curve Find the point P on the curve r(t) that lies closest to P0 and state... Problem 58E: 5758. Closest point on a curve Find the point P on the curve r(t) that lies closest to P0 and state... Problem 59E: Curves on spheres 75. Graph the curve r(t)=12sin2t,12(1cos2t),cost and prove that it lies on the... Problem 60E Problem 61E Problem 62E: Closed plane curves Consider the curve r(t) = (a cos t + b sin t)i + (c cos t + d sin t)j + (e cos t... Problem 63E: Closed plane curves Consider the curve r(t) = (a cos t + b sin t)i + (c cos t + d sin t)j + (e cos t... Problem 64E: Closed plane curves Consider the curve r(t) = (a cos t + b sin t)i + (c cos t + d sin t)j + (e cos t... Problem 65E: Closed plane curves Consider the curve r(t) = (a cos t + b sin t)i + (c cos t + d sin t)j + (e cos t... Problem 66E: Limits of vector functions Let r(t) = (f(t), g(t), h(t). a. Assume that limtar(t)=L=L1,L2,L3, which... format_list_bulleted