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 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 Select one: The acute angle between tangent to the surface and the given line at the -1 4 point (0,3, 9) is į – cos V537 The normal to the surface at the point (0,3, 9) is 6 j - k. The line is normal to the surface. The...
4. (4 pts) Consider the
surface z=x2y+y3.(a) Find the normal direction of the tangent plane
to the surface through (1,1,2).(b) Find the equation of the tangent
plane in (a).(c) Determine the value a so that the vector−→v=−−→i+
2−→j+a−→k is parallel to the tangent plane in (a).(d) Find the
equation of the tangent line to the level curve of the surface
through (1,1).
4. (4 pts) Consider the surface z = z2y + y). (a) Find the normal direction of the...
3 4. (4 pts) Consider the surface z = z = x²y + y3. (a) Find the normal direction of the tangent plane to the surface through (1,1,2). (b) Find the equation of the tangent plane in (a). (e) Determine the value a so that the vector 7= -7+27 +ak is parallel to the tangent plane in (a). (d) Find the equation of the tangent line to the level curve of the surface through (1,1).
Let Select all that apply
Let z =f(x,y)= arctan(3x In(6) Select all that apply Your answer: The slope of the tangent line to the curve obtained by intersecting the 9 surface z =f(x,y) and plane x = 3 at the point (3,6) is 6(811n (36) + 1) + fxy 54x2In(6y)+3) y(18x2in(6) + 1)2 (fxx (4,2))-(fvx(4,2)) = 0 The slope of the tangent line to the curve obtained by intersecting the 3In(36) surface z = f(x,y) and plane x = 3 at...
Let M be a surface and 11 a plane that intersects M in a curve γ. Show that y is a geodesic if II is a plane of symmetry of M, i.e., the two sides are mirror images.
Let M be a surface and 11 a plane that intersects M in a curve γ. Show that y is a geodesic if II is a plane of symmetry of M, i.e., the two sides are mirror images.
(1 point) The plane x y + 2z = 8 intersects the paraboloid z = x2 + y in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin. Point farthest away occurs at ). Point nearest occurs at
(1 point) The plane x y + 2z = 8 intersects the paraboloid z = x2 + y in an ellipse. Find the points on this ellipse that are nearest to and farthest from...
Find the point, P, at which the line intersects the plane. x= -6 - 3t, y = -3- 9t, z= -6+ 4t: 8x + 2y +6z = 5 The point, P, at which the line intersects the plane is (00). (Simplify your answer. Type an ordered triple.)
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2b with b ER. (a) Prove that the tangent line of each curve in H at a point (r, y) with y / 0 has slope (b) Let y -f(x) be a...
5 and 6 please
5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)