Question

In: Math

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).

Expert Solution

(a)

(b)

milcah answered 2 years ago

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).

(b) Find the equation of the tangent line to the curve 8x^2y^3-5x^2+7y^3=10(x-3y) , at...

(b) Find the equation of the tangent line to the curve 8x^2y^3-5x^2+7y^3=10(x-3y) , at the point (2,-2). (c) Given T''=6x^2y^3-cosx+5y^2-siny+10x^2-e^-3x ; determine: T'=∫(T'')∂x T'=∫(T'')∂y (d) Solve the equation cosecxcosydy-10xdx=0 , separably.

Find an equation for the plane that is parallel to the plane 3x−2y+z=1 and contains the...

Find an equation for the plane that is parallel to the plane 3x−2y+z=1 and contains the point (2,0,−1). Write the equation in the form ax+by+cz=d.

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

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.

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)

write the equation of a line tangent to x^2y^2+y^3=2 at (1,1)

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)...