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).

Expert Solution

milcah answered 2 years ago

Given the surface x= (3 (y-1)^2)+ (2 (z+ 3)^2)+ 7. Find an equation of the tangent...

Given the surface x= (3 (y-1)^2)+ (2 (z+ 3)^2)+ 7. Find an equation of the tangent plane at the point(12,2,2) in four ways: a) By using the surface as given,x=h(y,z) b) By writing the surface as z=f(x,y)(only keep the square root whose sign corresponds to the point(12,2,2)). c) By writing the surface as y=g(x,z)(only keep the square root whose sign corresponds to the point(12,2,2)).

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.

1a.Find the equation of the tangent plane to the surface √ x + √y + √...

1a.Find the equation of the tangent plane to the surface √ x + √y + √ z = 4 at P(1, 1, 4). 1b.Let f be a function of x and y such that fx = 3x − 5y and fy = 2y − 5x, which of the following is always TRUE? a. (0, 0) is not a critical point of f. b. f has a local minimum at (0, 0) c. f has a local maximum at (0, 0)...

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.

a. Find the tangent plane to z=(10-x^2-2y^2)^2 at (1,2,1). b. Find the equation of the tangent...

a. Find the tangent plane to z=(10-x^2-2y^2)^2 at (1,2,1). b. Find the equation of the tangent plane to the level surface for w=x^2y+y^2z+xyz^2 when w=8 at (1,2,1).

Find the tangent plane to Z= xsin(x+y) at (1,1,0)

Find the equation of the plane tangent to the function f(x, y) = (x^2)(y^2) cos(xy) at...

Find the equation of the plane tangent to the function f(x, y) = (x^2)(y^2) cos(xy) at x = y = π / √ 2 . Using this linearization to approximate f, how good is the approximation L(x, y) ≈ f(x, y) at x = y = π / √ 2 ? At x = y = 0? At (x, y) = (π, π)?

2. (a) Find an equation of the tangent plane to the surface x4 +y4 +z4 =...

2. (a) Find an equation of the tangent plane to the surface x4 +y4 +z4 = 18 at (2, 1, 1). Find a derivative in direction (2,2,1) at point (2,1,1). (b) Use Lagrange multipliers to ﬁnd the minimum and maximum values of f(x,y,z) = 8x + y + z on the surface x4 + y4 + z4 = 18.

Find an equation for the tangent plane of the surface xy^2 + yz^2 − 2xz =...

Find an equation for the tangent plane of the surface xy^2 + yz^2 − 2xz = −3 at the point (2, −1, 1)

Find an equation of the tangent plane to g(x,y)=e^(4x) -2xy+y^3 at (0,1)

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