): Classify and sketch the quadric surface x2 +2x+92-.2+22+1 = 0, labeling at least 3 points on the surface. Show the trace of the graph in 3 planes. ): Classify and sketch the quadric surfac...
Exercise 3. Find and identify the trace of the given quadric surface in the specified plane of coordinates. f) x2 + 2y – 2z2 – 2 = 0, xz-plane. g) x = y2 + 4, xy-plane. a) A + B + * = 1, xy-plane. b) x2 + 4y2 – 4z2 – 16 = 0, xz-plane. c) -4x2 - y2 + z2 = 1, yz-plane. d) x2 + – z2 = 0, yz-plane. e) x2 + x2 – 4y+4= 0,...
8) Show that the graph of +692 +9z²&exy 6x z-12yz-2x - 4y +6z+1=0 is degenerate quadric whizh consists plare. nuestion.
1) Consider the surface x2 + 3y2-2z2-1 (a) What are the cross sections(traces) in x k,y k, z k Sketch for (b) Sketch the surface in space. 2) Draw the quadric surface whose equation is described by z2 +y2 - 221 (a) What are the cross sections(traces) inx-k,y k,z k Sketch for (b) Sketch the surface in space. a) Sketch the region bounded by the paraboloids z-22 + y2 and z - 3) 2 b) Draw the xy, xz, yz...
8. (b) Sketch the graph of f(x,y) = 1 - x2 - y2. Sketch the level curves of f(x,y,z) = k for f(x,y,z) = 2x - 3y + z-12, with k=0, 24, -12. - 22. 22
show all work thank you
4) (5pts) the region under the surface z x2+ y4, and bounded by the planes x-0 and y-9 4 2 and the cylinder y x
4) (5pts) the region under the surface z x2+ y4, and bounded by the planes x-0 and y-9 4 2 and the cylinder y x
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
1. Find parametric equations for each surface. a) The plane through the points (0, 0,0), b) The portion of the sphere x2 +y2 + c) The part of the cylinder y 16 (1,0,3), and (0, 2,3) 22-9 inside the first octant, that lies between the planes +4.
1. Find parametric equations for each surface. a) The plane through the points (0, 0,0), b) The portion of the sphere x2 +y2 + c) The part of the cylinder y 16 (1,0,3),...
1 3. (10 points) Let S be the quadratic surface given by 22-2-y (a) Classify S (B) S is a hyperboloid of one sheet (E) S is an (A) S is an (D) S is an (b) Find the equation of the tangent plane to S at the point (1,1, v3) (C) S is a hyperboloid of two sheets ellipsoid elliptic cone elliptic paraboloid point P(ro.Mo, 20) on S where the tangent plane to S at the point P contains...
4.
Graph the polar equation r = 2cos(2theta + pi/2) + 1 . You must
show all of your work and label at least 5 polar points.
(C) sketch the graph of y, with appropriate labeling of points as ordered pairs. One period will do. 4. Graph the polar equation r = 2 cos(20 + 8) + 1. You must show all of your work and label at least 5 polar points.. South folle
13. The graph of f is shown. State, with reasons, the numbers at which f is not continuous. a) State, with reasons, the numbers at which fis not differentiable. b) 246 0 4 14. Trace the graph of the function and sketch a graph of its derivative directly beneath. a) b) c) 0 any differentiation formulas to find equations of the tangent line and normal line to the curve y at the given point P a) y (2x-3)2 at P-(1,...