Find the equation for the tangent plane to the surface z=In(9x2 + 5y2+1 O x+y = 0 z = 0 O x-y = 0 O x+y+z = 0

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,v)…

A:

Q: Find an equation of the tangent plane to the given surface at specified point. a) z = e*y +…

A: Here To find the equation of the tangent plane to the given surface at specified points,  we will…

Q: Show that the curve r= Vti + Vtj + (2t – 1)k is tangent to the surface x +y² – z = 1 when t=1

A: Given that r=ti+tj+2t-1k and f=x2+y2-z-1 Take the derivative for f, ∇f=ddx,ddy,ddzf=2x,2y,-1…

Q: Find an equation of the plane tangent to the surface xy z = 2 at the point (2, 1, -1). O A.x + 6y +…

A:

Q: Find the area of the portion of the cylindrical surface Y = 4 – x² in the first octant that is…

A:

Q: Find an equation of the tangent plane to the given surface at the specified point z = sin(xy), (x,v)…

A:

Q: Find the tangent plane of the surface z = f(x, y) at (0,0, 0) in which 3y f(2, y) = || cos /3 t dt.

A:

Q: Consider x=h(y,z) as a parametrized surface in the natural way. Write the equation of the tangent…

A:

Q: ns: Find the tangent plane to the surface of x2 + z² = y² + 9 at (1, –1,3). 3

A: Follow the procedure given below.

Q: Find the equation of the tangent plane to *+ y? at the point (2, –3, 10) the surface z = 4 O x + 4y…

A: We have to find

Q: Let (S) be the surface given by the following equation. x²+y² = 1+ z?. An equation of the tangent…

A:

Q: Consider the surface z = x In y – x²y. (a) Show that Q = (1,1, –1) lies on this surface. (b) Find…

A: Consider the surface: z=xlny-x2y…

Q: Let (S) be the surface given by the following equation. x²+y? = 1+ z?. An equation of the tangent…

A:

Q: The slope of the tangent line to the curve of intersection of the plane r = zo and the surface z=…

A: In the given problem we have to find the slope of the tangent line to the curve of intersection of…

Q: Let F(x, y, z) = 15x? + 12y2 + 10z?. Find the equation to the tangent plane to the level of surface…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: An equation of the tangent plane to the surface z = In(x - 2y) at (3, 1,0) is given by z = x + 2y- 1…

A: This question is related to three dimensions geometry.

Q: Calculate F. dS where F = (e* sin y, e² cos y, yz²) S is the surface of the box bounded by the…

A:

Q: Find all points on the surface at which the tangent plane is horizontal. (a) z = x³y² (b) z = x² −xy…

A: (a). Given the surface z=x3y2,the tangent lane at a given point is given by :…

Q: Calculate F- dS where F = (e" sin y, e* cos y, yz²) S is the surface of the box bounded by the…

A:

Q: 2. Let z = f(x,y) = x³ + xe* +y?. (a) Find an equation of the tangent plane to the surface z = f(r,…

A:

Q: 4. Compute |F- dš, where F = (y, –x,2z) and S is the surface of the sphere of radius 2, centered at…

A:

Q: = xyz exists over a surface S c ed by the plane x-0,y%3D0,z%3D0, z=y V dS over the curve surface.

A: Given:  V= xyz x2+y2=9 To find: ∫s V ds  For solving the convergence x2+y2=9 (mod 1s) we use Chinese…

Q: . Show that the tangent plane to the surface 2yyo cz at the point P(xo,Y0, zo) is given by the 2rro…

A:

Q: Find an equation of the plane tangent to the surface xy z2 = 2 at the point (2, 1, -1). О А.х+ бу +…

A:

Q: The slope of the tangent line to the curve of intersection of the plane x = xo and the surface z =…

A: Proceed as shown below

Q: Calculate F - dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: Given F¯={exsiny,excosy,yz2)

Q: Let f(x,y)=x*e^(xy). Find the equation of the tangent plane to the surface z=f(x,y) at (1,0,1).

A: Formula:

Q: Calculate the positive value of m so that the x+y+2z=m plane is tangent to the spherical surface…

A:

Q: Find the equation of the tangent plane Pr to the surface S:r + y? + z? = 9 at (2, 1, –2) O Pr: 4x –…

A:

Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface…

A:

Q: Find the points on the surface xy + yz + zx - x- z =0 where the ant pla

A:

Q: Find an equation of the tangent plane to the given surface at specified poir a) z = e*y + yx²e!¬y);…

A: The formula for the tangent plane at the given point x0,y0,z0 is:…

Q: 4. Obtain the equation of the tangent plane to the surface with parametric representation r(u, v) =…

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: Consider a surface defined by F(, y, z) = 0 whose gradient is (cos(Tx), z? e", 2ze"). The equation…

A:

Q: 30. The equation of the tangent plane to the surface z = x? – 2y² at x = 1, y = 0 is (а) 2 — : 2т —…

A:

Q: 1) Let h(x, y) = x* – 4xy² – 2x² + 8y². Find and classify all local extrema of the surface using the…

A:

Q: Consider the surface defined by f (, y) = ln(5y – 7x). Find the equation of the tangent plane to…

A: Given: fx,y=ln5y-7x We have to find equation of tangent plane to fx,y at the point 2,3.

Q: Show that the tangent plane to the surface x 2 a 2 + y 2 b 2 = cz at the point P(x0, y0, z0) is…

A:

Q: Find the plane tangent to the given surfaces at the specific point. f(x, y) = ex(x cos y − y sen y)…

A:

Q: t the plane tangent to the smooth surface z = f(x, y) at (xo, Yo, f(xo, fz(x0, Yo)(x – ro) + fy(o,…

A: In this question we will use basic of calculus i.e application of vector calculus. Solution of the…

Q: Find f[fp Vx2 + y2 + z² dV, where D is the sphere of radius a centered at the origin.

A: We need to find the integral:∫∫∫Dx2+y2+z2dVwhere D is the sphere of radius a centered at the…

Q: Evaluate the area of the surface generated by revolving the curve y = 2/a, from x = 0 to x = 3. y -…

A:

Q: Find the equation of the tangent plane Pr to the surface S:r +y +z2 = 9 at (2,-1, 2) | O PT:4x + 2y…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: How many points are there on the surface z = dx +y such that the tangent plane to the surface is…

A: Given :  d=maxa,b,c⇒d=max2,1,0⇒d=2 So,z=dx2+y2⇒z=2x2+y2 Also, dx+y+z=0⇒2x+y+z=0 Let fx,…

Q: Calculate / F . dS where F = (e* sin y, e cos Y, yz²) S is the surface of the box bounded by the…

A:

Q: Use Stokes' Theorem to calculate fe F-dĩ, where F = zyi+3=j+5zk, and C is the closed path around a…

A: Here given that F→=xy i^+3z j^+5x k^ and curve C in xz-plane. To find: ∫C F→·dr→ by Stokes' theorem.

Q: Find the equation of the tangent plane to the given surface at the specified point. z+7=xecosz,…

A: Given: z+7=xeycosz,  (7,0,0)