If
x2 + xy + y3 = 1,find the value ofy'''at the point wherex = 1If x2 + xy + y3 = 1, find the value of y''' at the point where x = 1
Find an equation for the line tangent to the graph of y=x3+ √xy + y3=3 at the point (1,1).
Find Vf at the given point. f(x,y,z) = x2 + y3 – 322 + z Inx, (1,1,4) Vf|(1,1,4) = i+ )j + (O)k (Simplify your answers.)
Given F(x, y) = (x²y3, xy). (a) Determine if F is conservative. If yes, find the scalar potential. (b) Evaluate F.dr where is the path defined parametrically by r(t) = (13 – 2t, t3 + 2t) e/F c for 0 < t < 1.
2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction
2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction
1. Find the equation of the tangent line to: a) y = x2 – 3 at the point (2,1) b) y = cos x at the point (1,1) c) y=e" at the point where r = 1 d) r3 + y3 = 19 at the point (3,-2) 2. Find the equation of the normal line to: a) y = r at the point (2,8) b) y=x+ at the point where x = 2 c) y = 2:03 - 5x +...
Let g(x, y, z) = x2 + xy + xyz?. (a) Find the gradient of g. (b) Find the rate of change of g at the point (1,-1,2) in the direction of the vector v = (8,4,-1).
The temperature at any point (x, y, z) in space is T = x y3 z4 Find the highest temperature on the surface 4 x2 + 4 y2 + z2 = 8. Enter the exact value of your answer in the box below. Warning: If your answer involves a square root, use either sqrt or power 1/2. Note: The highest temperature cannot be 0.
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
(1 point Find the volume of the solid that lies within the sphere x2 + 2 + z-64 above the xy plane, and outside the cone z 8V x2 y2
(1 point Find the volume of the solid that lies within the sphere x2 + 2 + z-64 above the xy plane, and outside the cone z 8V x2 y2
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....