
x2 Find the x and y intercepts for the equation y2 23.(2 pts.) 4 25 x-intercepts...
0 3.2.69) Find the x-intercepts and y-intercepts of the circle x2 + y2-4x- 6y +4 3.4.25) Find the domain of f (x)9x 3.6.1) Find the equation of any parabola that has vertex V(-3, 1) x+1
Find the x- and y-intercepts of the graph of the equation. x = -y2 + 7 x-intercept (x, y) = ( (smaller y-value) y-intercept (x, y) = ( y-intercept (x, y) = ( (I ) (larger y-value)
2: (a) Find all solutions (x, y) = Z2 to Pell's Equation x2 – 29 y2 = 1. (b) Find all solutions (x, y) € Z to the Pell-like equation x2 - 21 y2 = 4.
24) a. Find the x intercepts for the parabola whose equation is: b. Find the y intercept for the parabola whose equation is: y x2-7x +10 25) If f(x) 5x +4, find f(5)
Consider the following equation. y2 - x = 36 Find any intercepts. x-intercept (x, y) =( ) y-intercepts (x, y) = ( ) (smaller y-value) (X. ) = ( ) (larger y-value) x-intercept (x, y) (larger y-value) Test for symmetry. (Select all that apply.) The equation is symmetric with respect to the x-axis. U The equation is symmetric with respect to the y-axis. U The equation is symmetric with respect to the origin. None of the above. Sketch the graph...
(23 pts) Let F(x, y, z) = ?x + y, x + y, x2 + y2?, S be the top
hemisphere of the unit sphere oriented upward, and C the unit
circle in the xy-plane with positive orientation.
(a) Compute div(F) and curl(F).
(b) Is F conservative? Briefly explain.
(c) Use Stokes’ Theorem to compute ? F · dr by converting it to
a surface integral. (The integral is easy if C
you set it up correctly)
4. (23 pts)...
6 (20 pts). Let F(x, y, z) = x2 + y2 + x2 - 6xyz. (1) Find the gradient vector of F(x, y, z); (2) Find the tangent plane of the level surface F(x, y, z) = x2 + y2 + x2 - 6xyz = 4 at (0, 0, 2); (3) The level surface F(x, y, z) = 4 defines a function z = f(x,y). Use linear approxi- mation to approximate z = = f(-0.002,0.003).
Find the general solution of the differential equation xy' = y + (x2 + y2 y(4) = 3
6. Find the equation of the tangent line at the given point. (a) x2 + y2 = 25,(-3, 4) (b) 2y - Vt = 4,(16, 2) (c) y + xy² + 1 = x + 2yº, x = 2
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.