Problem 1E: Find dy/dx. 1. x=t1+t,y=1+t Problem 2E: Find dy/dx. 2. x = tet, y = t + sin t Problem 3E: Find an equation of the tangent to the curve at the point corresponding to the given value of the... Problem 4E: Find an equation of the tangent to the curve at the point corresponding to the given value of the... Problem 5E: Find an equation of the tangent to the curve at the point corresponding to the given value of the... Problem 6E: Find an equation of the tangent to the curve at the point corresponding to the given value of the... Problem 7E: Find an equation of the tangent to the curve at the given point by two methods: (a) without... Problem 8E: Find an equation of the tangent to the curve at the given point by two methods: (a) without... Problem 9E: Find an equation of the tangent to the curve at the given point. Then graph the curve and the... Problem 10E: Find an equation of the tangent to the curve at the given point. Then graph the curve and the... Problem 11E: Find dy/dx and d2y/dx2. For which values of t is the curve concave upward? 11. x = t2 + 1, y = t2 +... Problem 12E: Find dy/dx and d2y/dx2. For which values of t is the curve concave upward? 12. x = t3 + 1, y = t2 t Problem 13E: Find dy/dx and d2y/dx2. For which values of t is the curve concave upward? 13. x = et, y = tet Problem 14E: Find dy/dx and d2y/dx2. For which values of t is the curve concave upward? 14. x = t2 + 1, y = et 1 Problem 15E: Find dy/dx and d2y/dx2. For which values of t is the curve concave upward? 15. x = t ln t, y = t +... Problem 16E: Find dy/dx and d2y/dx2. For which values of t is the curve concave upward? 16. x = cos t, y = sin... Problem 17E: Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing... Problem 18E: Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing... Problem 19E: Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing... Problem 20E: Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing... Problem 21E: Use a graph to estimate the coordinates of the rightmost point on the curve x = t t6, y = et. Then... Problem 22E Problem 23E: Graph the curve in a viewing rectangle that displays all the important aspects of the curve. 23. x =... Problem 24E: Graph the curve in a viewing rectangle that displays all the important aspects of the curve. 24. x =... Problem 25E: Show that the curve x = cos t, y = sin t cos t has two tangents at (0, 0) and find their equations.... Problem 26E Problem 27E: (a) Find the slope of the tangent line to the trochoid x = r d sin , y = r d cos in terms of .... Problem 28E: (a) Find the slope of the tangent to the astroid x = a cos3, y = a sin3 in terms of . (Astroids are... Problem 29E: At what point(s) on the curve x = 3t2 + 1, y = t3 1 does the tangent line have slope12? Problem 30E: Find equations of the tangents to the curve x = 3t2 + 1, y = 2t3 + 1 that pass through the point (4,... Problem 31E: Use the parametric equations of an ellipse, x = a cos , y = b sin , 0 2, to find the area that it... Problem 32E: Find the area enclosed by the curve x = t2 2t, y=t and the y-axis. Problem 33E: Find the area enclosed by the x-axis and the curve x = t3 + 1, y = 2t t2. Problem 34E: Find the area of the region enclosed by the asteroid x = a cos3, y = a sin3. (Astroids are explored... Problem 35E: Find the area under one arch of the trochoid of Exercise 10.1.40 for the case d r. Problem 36E: Let be the region enclosed by the loop of the curve in Example 1. (a) Find the area of . (b) If is... Problem 37E: Set up an integral that represents the length of the curve. Then use your calculator to find the... Problem 38E: Set up an integral that represents the length of the curve. Then use your calculator to find the... Problem 39E: Set up an integral that represents the length of the curve. Then use your calculator to find the... Problem 40E Problem 41E: Find the exact length of the curve. 41. x = 1 + 3t2, y = 4 + 2t3, 0 t 1 Problem 42E: Find the exact length of the curve. 42. x = et t, y = 4et/2, 0 t 2 Problem 43E: Find the exact length of the curve. 43. x = t sin t, y = t cos t, 0 t 1 Problem 44E: Find the exact length of the curve. 44. x = 3 cos t cos 3t, y = 3 sin t sin 3t, 0 t Problem 45E: Graph the curve and find its exact length. 45. x = et cos t, y = et sin t, 0 t Problem 46E: Graph the curve and find its exact length. 46. x=cost+ln(tan12t), y = sin t, /4 t 3/4 Problem 47E: Graph the curve x = sin t + sin 1.5t, y = cos t and find its length correct to four decimal places. Problem 48E: Find the length of the loop of the curve x = 3t t3, y = 3t2. Problem 49E Problem 50E: In Exercise 10.1.43 you were asked to derive the parametric equations x = 2a cot , y = 2a sin2 for... Problem 51E: Find the distance traveled by a particle with position (x, y) as t varies in the given time... Problem 52E: Find the distance traveled by a particle with position (x, y) as t varies in the given time... Problem 53E: Show that the total length of the ellipse x = a sin , y = b cos , a b 0, is L=4a0/21e2sin2d where... Problem 54E Problem 55E: (a) Graph the epitrochoid with equations x = 11 cos t 4 cos(11t/2) y = 11 sin t 4 sin(11t/2) What... Problem 57E: Set up an integral that represents the area of the surface obtained by rotating the given curve... Problem 58E Problem 59E Problem 60E Problem 61E: Find the exact area of the surface obtained by rotating the given curve about the x-axis. 61. x =... Problem 62E: Find the exact area of the surface obtained by rotating the given curve about the x-axis. 62. x =... Problem 63E: Find the exact area of the surface obtained by rotating the given curve about the x-axis. 63. x = a... Problem 64E Problem 65E: Find the surface area generated by rotating the given curve about the y-axis. 65. x = 3t2, y = 2t3,... Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E Problem 71E Problem 72E Problem 73E Problem 74E: A cow is tied to a silo with radius r by a rope just long enough to reach the opposite side of the... format_list_bulleted