Let z = x2 + y2 be the surface, and x = -1+t, y= 2+t, z = 2t + 7 be the line. Find the incorrect answer in the following 4 Select one: The acute angle between tangent to the surface and the given line at the -1 point (0,3,9) is į – cos V6 37 The normal to the surface at the point (0,3, 9) is 6 j-k. The line is normal to the surface. The line intersects at...
Let f(x, y) = x²y + 5yº. At the point (1, -2), which one is incorrect about the behaviour of the function f: Select one: f(x, y) is decreasing at the rate of 4 units per unit increase in X. f(x, y) is increasing at the rate of 61 units per unit increase in y o the slope of the surface Z = f(x,y) in the y, direction is 61 f(x,y) is increasing at the rate of 4 units per...
Let F(r, y, z)(z4+ 5y3)i + (y2 surface of the solid octant of the sphere x2+yj2 + 22 = 9 for x> 0, y> 0 and z> 0 )j+ (3z + 7)k be the velocity field of a fluid. Let B be the Determine the flux of F through B in the direction of the outward unit normal Let F(r, y, z)(z4+ 5y3)i + (y2 surface of the solid octant of the sphere x2+yj2 + 22 = 9 for x>...
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).
Consider the following. z = x2 + y2, z = 36 − y, (6, -1, 37) (a) Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the given point. x − 6 12 = y + 1 −2 = z − 37 −1 x − 6 1 = y + 1 12 = z − 37 −12 x − 6 = y + 1 = z − 37 x − 6 12 =...
Chapter 13, Section 13.7, Question 017 (a) Find all points of intersection of the line x = -2+1, y = 3 +t, z = 2t +21 and the surface z= x2 + y2 (b) At each point of intersection, find the cosine of the acute angle between the given line and the line normal to the surface. Enter your answers in order of ascending x-coordinate value. (a) (b) (x1,91,21) = (003 Edit cos 01 = ? Edit (x2, Y2, 22)...
Consider the following. w = In(x2 + y), x = 2t, y = 5 - t (a) Find af by using the appropriate Chain Rule. (b) Find by converting w to a function of t before differentiating. -/1 POINTS LARCALC11 13.R.054. Differentiate implicitly to find oux x2 = 9 x + y -11 POINTS LARCALC11 13.R.069. Find an equation of the tangent plane to the surface at the given point. z = x2 + y2 + 9, (1, 2, 14)
(1 point) A parametric curve r(t) crosses itself if there exist t s such that r(t)-r(s). The angle of intersection is the (acute) angle between the tangent vectors r() and r'(s). The parametric curver (2 -2t 3,3 cos(at), t3 - 121) crosses itself at one and only one point. The point is (r, y, z)-5 3 16 Let 0 be the acute angle between the two tangent lines to the curve at the crossing point. Then cos(0.997 (1 point) A...
At what point on the surface z = 2 + x2 + y2 is its tangent plane parallel to the following planes? (a) z = 6 (x, y, z) = (b) z = 6 + 4x − 12y (x, y, z) =
(b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the curve from above. point in the anti-clockwise direction when viewed Calculate the line integral (e (e sin y+ 4) dy+(e(cos z+ sin z)+ay) dz. cos x2yz) dx + (b) Let C be the closed curve formed by intersecting the cylinder x2 +y= 1 with the plane x z= 2. Let the tangent to the...