Suppose that ? is the intersection of the plane ?+?+3?=4 and the surface ?^2−?^2=?^2−8 . Note...

Suppose that ? is the intersection of the plane ?+?+3?=4 and the surface ?^2−?^2=?^2−8 . Note that this intersection contains the point (3,4,−1) . Verify the assumptions of the implicit function theorem at this point; then if ?(?)=(?,?) φ ( x ) = ( y , z ) be the function from ℝ→ℝ2 R → R 2 verifying the conclusion of the implicit function theorem, compute ??(3) J φ ( 3 ) using the theorem. Verify your conclusion by explicitly solving for (?,?) ( y , z ) in terms of ? x and differentiating.

Expert Solution

Colby Messinger answered 2 years ago

The surface z = 3x^(2) + (1/6)x^(3) - (1/8)x^(4) - 4y^(2) is intersected by the plane...

The surface z = 3x^(2) + (1/6)x^(3) - (1/8)x^(4) - 4y^(2) is intersected by the plane 2x - y = 1. The resulting intersection is a curve on the surface. Find a set of parametric equations for the line tangent to this curve at the point (1,1,-23/24).

Find the mass of the solid bounded by the ??-plane, ??-plane, ??-plane, and the plane (?/2)+(?/4)+(?/8)=1,...

Find the mass of the solid bounded by the ??-plane, ??-plane, ??-plane, and the plane (?/2)+(?/4)+(?/8)=1, if the density of the solid is given by ?(?,?,?)=?+3?.

find the point lying on the intersection of the plane, x + (1/4)y + (1/3)z =...

find the point lying on the intersection of the plane, x + (1/4)y + (1/3)z = 0 and the sphere x 2 + y 2 + z 2 = 25 with the largest z-coordinate. (x,y,z)=(_)

8. (a) Classify the quadric surface 4? 2 − ? + 2? 2 = 0. [4...

8. (a) Classify the quadric surface 4? 2 − ? + 2? 2 = 0. [4 points] (b) Find the traces of the above surface in xy, xz, yz-plane respectively. [6 points]

Find the equation of the tangent plane to the surface x + y^2 + z^3 +...

Find the equation of the tangent plane to the surface x + y^2 + z^3 + sin(x − yz) = 7 at the point (2, 2, 1).

Find the equation of the tangent plane to the surface, (4x^2)(y^3) + (5yz) + (2xz^3) =...

Find the equation of the tangent plane to the surface, (4x^2)(y^3) + (5yz) + (2xz^3) = 7 at the point P(-1,1,1). Also nd the parametric equation of the normal line to that surface at that point . Sketch a picture that illustrates what this is all about.

Find the point (s) on the surface function ??^2 ?^3 = 3 + 8 + 6...

Find the point (s) on the surface function ??^2 ?^3 = 3 + 8 + 6 that are closest to the origin.

12a Find an equation of the tangent plane to the surface ? = 2? 2 +...

12a Find an equation of the tangent plane to the surface ? = 2? 2 + ? 2 − 5?, ?? (1, 2, −4). 12b If ? = ? 2 − ?? + 3? 2 and (?, ?) changes from (3, −1) to (2.96, −0.95), compare ∆? and ??. Calculus 3 question. Please help.

Suppose that a population consists of the six values 4, 8, 5, 3, 8, and 4....

Suppose that a population consists of the six values 4, 8, 5, 3, 8, and 4. (a) Find the population mean and variance. (b) Calculate the sampling distribution of the mean of a sample of size 3 by displaying all possible such samples (chosen without replacement). (c) Use the results from (b) to find the mean and variance of the sampling distribution. (d) Compare the answers from (c) with those obtained from the general formulas for E(X) and Var(X) derived...

Find an equation of the tangent plane to the surface x5+5z2ey−x=848 at point P=(3, 4, 11e√)....

Find an equation of the tangent plane to the surface x5+5z2ey−x=848 at point P=(3, 4, 11e√). (Use symbolic notation and fractions where needed. Your answer should be in the form ax+by+cz=1.)

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