Problem 1QCE Problem 2QCE: The graph of the curve described by the parametric equations x=4t1,y=3t+2 is a straight line with... Problem 3QCE: Suppose that a parametric curve C is given by the equations x=ft,y=gtfor0t1. Find parametric... Problem 4QCE: To find dy/dx directly from the parametric equations x=ft,y=gt we can use the formula dy/dx=. Problem 5QCE: Let L be the length of the curve x=lnt,y=sint1t An integral expression for L is . Problem 1ES: (a) By eliminating the parameter, sketch the trajectory over the time interval 0t5 of the particle... Problem 2ES: (a) By eliminating the parameter, sketch the trajectory over the time interval 0t1 of the particle... Problem 3ES: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t.... Problem 4ES: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t.... Problem 5ES: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t.
Problem 6ES: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t.... Problem 7ES Problem 8ES: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t.... Problem 9ES: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t.
Problem 10ES: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t.... Problem 11ES: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t.... Problem 12ES: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t.... Problem 13ES Problem 14ES Problem 15ES: Find parametric equations for the curve, and check your work by generating the curve with a graphing... Problem 16ES: Find parametric equations for the curve, and check your work by generating the curve with a graphing... Problem 17ES: Evaluation Warning: The document was created with Spire.Doc for .NET. Find parametric equations for... Problem 18ES Problem 19ES: (a) Use a graphing utility to generate the trajectory of a housefly whose equations of motion over... Problem 20ES: (a) Use a graphing utility to generate the trajectory of a paper airplane whose equations of motion... Problem 21ES Problem 22ES: Graph the equation using a graphing utility. ax=y+2y3y5bx=tany,/2y/2 Problem 23ES: In each part, match the parametric equation with one of the curves labelled (I)-(VI), and explain... Problem 24ES: (a) Identify the orientation of the curves in Exercise 23. (b) Explain why the parametric curve... Problem 25ES: (a) Suppose that the line segment from the point Px0,y0toQx1,y1 is represented parametrically by... Problem 26ES: Find parametric equations for the line segment joining P2,1andQ3,1, and use the result in Exercise... Problem 27ES: (a) Show that the line segment joining the points x0,y0andx1,y1 can be represented parametrically as... Problem 28ES: (a) By eliminating the parameter, show that if a and c are not both zero, then the graph of the... Problem 29ES: Use a graphing utility and parametric equations to display the graph of f and f1 on the same screen.... Problem 30ES: Use a graphing utility and parametric equations to display the graph of f and f1 on the same screen.... Problem 31ES: Use a graphing utility and parametric equations to display the graph of f and f1 on the same screen.... Problem 32ES: Use a graphing utility and parametric equations to display the graph of f and f1 on the same screen.... Problem 33ES: Determine whether the statement is true or false. Explain your answer. The equation y=1x2 can be... Problem 34ES: Determine whether the statement is true or false. Explain your answer. The graph of the parametric... Problem 35ES: Determine whether the statement is true or false. Explain your answer. For the parametric curve... Problem 36ES Problem 37ES: Parametric curves can be defined piecewise by using different formulas for different values of the... Problem 38ES: Find parametric equations for the rectangle in the accompanying figure, assuming that the rectangle... Problem 39ES: (a) Find parametric equations for the ellipse that is centered at the origin and has intercepts... Problem 40ES: We will show later in the text that if a projectile is fired from ground level with an initial speed... Problem 41ES: (a) Find the slope of the tangent line to the parametric curve x=t/2,y=t2+1att=1andt=1 without... Problem 42ES: (a) Find the slope of the tangent line to the parametric curve x=3cost,y=4sintatt=/4andatt=7/4... Problem 43ES: For the parametric curve in Exercise 41, make a conjecture about the sign of d2y/dx2att=1andatt=1,... Problem 44ES: For the parametric curve in Exercise 42, make a conjecture about the sign of... Problem 45ES: Find dy/dxandd2y/dx2 at the given point without eliminating the parameter. x=t,y=2t+4;t=1 Problem 46ES: Find dy/dxandd2y/dx2 at the given point without eliminating the parameter. x=12t2+1,y=13t3t;t=2 Problem 47ES: Find at the given point without eliminating the parameter.
Problem 48ES: Find at the given point without eliminating the parameter.
Problem 49ES: Find dy/dxandd2y/dx2 at the given point without eliminating the parameter. x=+cos,y=1+sin;=/6 Problem 50ES: Find dy/dxandd2y/dx2 at the given point without eliminating the parameter. x=cos,y=3sin;=5/6 Problem 51ES: (a) Find the equation of the tangent line to the curve x=et,y=etatt=1 without eliminating the... Problem 52ES: (a) Find the equation of the tangent line to the curve x=2t+4,y=8t22t+4att=1 without eliminating the... Problem 53ES: Find all values of t at which the parametric curve has (a) a horizontal tangent line and (b) a... Problem 54ES: Find all values of t at which the parametric curve has (a) a horizontal tangent line and (b) a... Problem 55ES: In the and-1850s the French physicist Jules Antoine Lissajous (1822-1880) became interested in... Problem 56ES: The prolate cycloid x=2cost,y=2tsintt crosses itself at a point on the x-axis (see the accompanying... Problem 57ES: Show that the curve x=t2,y=t34t intersects itself at the point (4, 0), and find equations for the... Problem 58ES: Show that the curve with parametric equations x=t23t+5,y=t3+t210t+9 intersects itself at the point... Problem 59ES Problem 60ES: Verify that the cycloid described by Formula (10) has cusps at its x-intercepts and horizontal... Problem 61ES: (a) What is the slope of the tangent line at time t to the trajectory of the paper airplane in... Problem 62ES: Suppose that a bee follows the trajectory x=t2cost,y=22sint0t10 (a) At what limes was the bee flying... Problem 63ES: Consider the family of curves described by the parametric equations x=acost+h,y=bsint+k0t2 where... Problem 64ES: (a) Use a graphing utility to study how the curves in the family x=2acos2t,y=2acostsint2t2 change as... Problem 65ES: Find the exact arc length of the curve over the stated interval.
Problem 66ES: Find the exact arc length of the curve over the stated interval. x=t2,y=2t3/41t16 Problem 67ES: Find the exact arc length of the curve over the stated interval. x=cos3t,y=sin3t0t Problem 68ES: Find the exact arc length of the curve over the stated interval. x=sint+cost,y=sintcost0t Problem 69ES: Find the exact arc length of the curve over the stated interval.
Problem 70ES: Find the exact arc length of the curve over the stated interval. x=2sin1t,y=ln1t20t12 Problem 71ES Problem 72ES: Use the parametric equations in Formula (10) to verify that the cycloid provides one solution to the... Problem 73ES Problem 74ES: (a) If a thread is unwound from a fixed circle while being held taut (i.e., tangent to the circle),... Problem 75ES: If ftandgt are continuous functions, and if no segment of the curve x=ft,y=gtatb is traced more than... Problem 76ES: If ftandgt are continuous functions, and if no segment of the curve x=ft,y=gtatb is traced more than... Problem 77ES: If ftandgt are continuous functions, and if no segment of the curve x=ft,y=gtatb is traced more than... Problem 78ES: If ftandgt are continuous functions, and if no segment of the curve x=ft,y=gtatb is traced more than... Problem 79ES: If ftandgt are continuous functions, and if no segment of the curve x=ft,y=gtatb is traced more than... Problem 80ES: If ftandgt are continuous functions, and if no segment of the curve x=ft,y=gtatb is traced more than... format_list_bulleted