Convert the rectangular equation to polar form and select its graph. x2+y2 16
Convert the rectangular equation to polar form and select its graph. x2+y2 16
Convert the equation to polar coordinates. x2 + y2 = 7y + X Sketch the graph.
calc3
#9
9. Find the integral of x2 + y2 over the region defined by 0 Szs 2, x2 + y2 s1 the auha 10 21 YIO 21 Y 21
solve for dy/dx: x2 + xy3 - y + y2 = 9
Find the volume of the solid bounded on top by sphere x2+y2+z2= 9 , on the bottom by the plane z = 0, around the side by the cylinder x2+y2= 4.
Evaluate the integral by changing to cylindrical coordinates. 13 /9-x² 89-x² - y2 x2 + y2 dz dy dx Jo
For the limaçon x2 + y2 = (x2 + y2 - 2x)? (Exercise 24 in Section 3.5), verify that the points P(1.0) and 0(3,0) are on the graph and are the rightmost points (tangent line is vertical). (a) plug in x=1, y=0, both sides of the equation are equal to (b) plug in x=3, y=0, both sides of the equation are equal to (c) Find y'at P(1,0): y'I=1.y=0 = (d) Find y' at Q(3,0): y'Ix=3.y=0 =
The region R is bounded by the following curves. x2 + y2 = 4 x2 + y2 = 9 x2 - y2 = 1 x2 - y2 = 4 (a) Find a change of variables such that the transformed region is a rectangle in the uv-plane. u= V= (b) Draw a picture of S, the transformation of R into the uv-plane. Y υ 3 10 8 2 6 R 4 1 N х и 4 6 8 10 N (c)...
(a) Find and identify the traces of the quadric surface x2 + y2 ? z2 = 25 given the plane. x = k Find the trace. Identify the trace. y=k Find the trace. Identify the trace. z=k Find the trace Identify the trace. (b) If we change the equation in part (a) to x2 ? y2 + z2 = 25, how is the graph affected? (c) What if we change the equation in part (a) to x2 + y2 +...
Let Surface S be that portion of the sphere x2 + y2 + z2 = 9, which is above the plane z = 1. Parametrize this surface and write your final answer in vector function notation.