Find and sketch the projections of the curve on the three coordinate planes.
r(t) = (sin(t), t, 2cos(t))
Find and sketch the projections of the curve on the three coordinate planes.
(1) Draw the Projections of the curve on the three coordinate planes. Use these projections to help sketch the curve. (Hint: a Calculator in parametric mode could help with the first part.)(2) At what points does the curve intersect the paraboloid
please solve 9 and extra credit: find the volume of the solid bounded by the three coordinate planes and the plane 6x + 8y + 2z - 24 = Problem 9. Find the largest possible volume of the rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane 3r +y+2z 12. Problem ro. Compute the integral (sncos y)drdy. Extra Problem. Find the volume of the solid bounded by the three coordinate...
(3) Find the volume of the region bounded by the three coordinate planes and the surface va+ Vy+vz=1. Give a full-sentence explanation of your setup and change of variables, but then you can just show the computation of the integral.
find T,N,B curvature and torsion as a function of t for the space curve r(t)=sin t i+√2 cos t j+sin t k and find equation of normal and osculating planes
Find a vector function P(1) that parameterizes the curve of intersection of the cyinder X*+ --- = 1 and the plane 2x+y+z=1 • F(t)=(cos(t), 1-2cos(t) - sin(t), sin(t)> • F(t) = (cos(t), 1 - 2cos(t) – 3sin(t), 3sin(t)> • F(t) = (cos(t), sin(t), 1 – 2cos(t) - sin(t)> • F(t) = (cos(t), 3sin(t), 1-2cos(t) – 3sin(t)>
Sketching a Curve In Exercises 9-12, sketch the curve represented by the vector-valued function and give the orientation of the curve. 2 9. r(t) = (n cost, i sin ) 10. r(t) = (1 + 2.12 - 1) 11. r(t) = (1 + 1)i + (31 - 1)j + 2tk 12. r(t) = 2 cos ti + tj + 2 sin tk 29 12. r(t) = 2 cos ti + tj + 2 sin tk
The figure below shows a curve C, parametrized by (a) The point P lies on C, and its r-coordinate is 4. Find the value of t at the point P according to the parametrization, and find the y-coordinate of P. equation in terms of r and y. line 4. as shown shaded in the figure. Find the area of R. (b) The line is normal to C at the point P. Express the line l using an (c) The bounded...
5. Sketch the following graphs on four different coordinate planes. What message can you read? Cut on |||53|y|s3 lal+by1 = 1 y = 11 V VP-4y2 +3y = 0
Find the volume of the region in the first octant bounded by the coordinate planes , the plane y+z=3, and the cylinder x=9-y2
Sketch the space curve represented by the vector-valued function and give the orientation of the curve. r(t) = 5 cos(t)i + 5 sin(t)j + tk o op Tul Tul V - 5 y - 5