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All Textbook Solutions for Calculus Volume 2
For the following exercises, find the polar equation for the curve given as a Cartesian equation. 333. y2=4+x2Fur the following exercises, find the equation of the tangent line to the given curve. Graph both the function and its tangent line. 334. x=In(t),y=t21,t=1Fur the following exercises, find the equation of the tangent line to the given curve. Graph both the function and its tangent line. 335. r=3+cos(2),=34Fur the following exercises, find the equation of the tangent line to the given curve. Graph both the function and its tangent line. 336. Find dydx,dxdy and d2xdy2 of y=(2+et),x=1sin(t)For the following exercises, find the area of the region. 337. x=t2,y=In(t),0teFor the following exercises, find the area of the region. 338. r=1sin in the first quadrantFor the following exercises, find the arc length of the curve over the given interval. 339. x=3t+4,y=9t2,0t3For the following exercises, find the arc length of the curve over the given interval. 340. r=6cos,02 . Check your answer by geometry.For the following exercises, find the Cartesian equation describing the given shapes. 341. A parabola with focus (2, 5) and directrix x = 6For the following exercises, find the Cartesian equation describing the given shapes. 342. An ellipse with a major axis length of 10 and foci at (7, 2) and (1, 2)For the following exercises, find the Cartesian equation describing the given shapes. 343. A hyperbola with vertices at (3, 2) and (5, 2) and foci at (2, 6) and (2, 4)For the following exercises, determine the eccentricity and identify the conic. Sketch the conic. 344. r=61+3cos()For the following exercises, determine the eccentricity and identify the conic. Sketch the conic. 345. r=432cosFor the following exercises, determine the eccentricity and identify the conic. Sketch the conic. 346. r=755cosDetermine the Cartesian equation describing the orbit of Pluto, the- most eccentric orbit around the Sun. The length of the major axis is 39.26 AU and minor axis is 38.0? AU. What is the eccentricity?The C/1980 E1 comet was observed in 1980. Given an eccentricity of 1.057 and a perihelion (point of closest approach to the Sun) of 3.364 AU, find the Cartesian equations describing the comet’s trajectory. Are we guaranteed to see this comet again? (Hint: Consider the Sun at point (0, 0).