The equation of the tangent plane to the surface X(u, v) = (u + v)e, + (u – v)ez – uve; at X(1, –1) is : y +z = 1 z - x = 1 The above answer The above answer x + y+z = -1 x + y+z = 1 O The above answer O The above answer

Q: 1. Let k be a nonzero constant. Show that the equation of the tangent plane to the surface xyz = k…

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Q: Let z = g(x, y) = f(3 cos(xy), y + e#y) provided that f(3, 4) = 5, f1(3,4) = 2, f2(3, 4) = 5. i)…

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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: Consider the surface S: √x + √y + √z = a with a> 0. If P (x0, y0, z0) is a point on the surface that…

A: (a) The given surface S:x+y+z=a. Consider the level curve Fx,y,z=a  and a>0. Let Px0,y0,z0 is a…

Q: 6. Consider the paraboloid r(u, 0) = (u sin 0, u cos 0, u²). %3D There is a curve on the surface…

A: follow next step

Q: Let z = g(x, y) = f(3 cos(xy), y+ey) provided that f(3,5) = 3, f1(3,5) = 2, f2(3, 5) = 4. i) Find…

A: In this question we have to find following parts.

Q: The equation of the tangent plane to the surface f (x, y, z) = xe cosz - z -1= 0 at the point…

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Q: Let z = g(x, y) = f(3 cos(ry), y + ev) provided that f(3, 6) = 4, fi(3, 6) = 2, f2(3, 6) = 3. %3D i)…

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Q: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 5) = 8, f1(3, 5) = 2, f2(3, 5) = 3. %3D i)…

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Q: U SIII u' cos u?, EXAMPLE 6.6.3 For a surface of revolution defined by x u! oin o? COS 3 flol) aub…

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Q: Let z = g(x, y) = f(3 cos(xy), y +e²) provided that f(3, 6) = 6, fı(3,6) = 2, f2(3, 6) = 4. %3| %3|…

A: Given: g(x,y)=f3cosxy,y+exy Let gx,y=f(u,v) where u=3cosxy and v=y+exy so g is a function x,y where…

Q: Consider the equation of the surface S given by: ln(x2yz3) + xz − x2y = 0 An equation for the…

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Q: Let z = g(x, y) = f(3 cos(ry), y + e*) provided that f(3, 6) = 6, f1(3,6) = 2, f2(3, 6) = 4. i) Find…

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Q: 2) Consider the surface z = f(x, y) = xy - y?. a) Find the derivative of f at (1,2,-2) in the…

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Q: b) Consider z = z(x, y) as a function of x and y, so z(1, 0) = -1. Use the approximation of the…

A: The equation of the tangent plane is 3x-9y+z-2=0.  Then, the function is z=-3x+9y+2 The…

Q: Q1: Find the tangent plane and normal line of the surface F(x,y,z)=x² + n + y² + z² 10 at point…

A: We have to calculate partial derivatives first.

Q: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 6) = 7, fi(3, 6) = 2, f2(3,6) = 3. i) Find…

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Q: Find the surface arca of y = (1/3)r 10<x <1 revolved about the z-ax

A: Given: The equation is y = 13x3 , 0 ≤x≤1 revolved about the x - axis.

Q: Question 3 please

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Q: The equation of the tangent plane to the surface f (x,y, z) = xe cosz – z-1 = 0 at the point…

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Q: Let z = g(x, y) = f(3 cos(xy), y + e) provided that f(3,5) = 6, f1(3, 5) = 2, f2(3, 5) = 6. %3D i)…

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Q: 2. A surface S in R'(z,y, =) is defined parametrically in the form u + -1 -( ) X(u, e) = 2u 2 (a)…

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Q: 3. Consider the surface z = xln y – x²y. (a) Show that Q = (1,1, –1) lies on this surface. (b) Find…

A: The given surface is z=xlny-x2y (a) Substitute (x,y,z)=(1,1,−1) in z=xlny-x2y.…

Q: (a) Find an equation of the tangent plane to the surface at the given point. хуz %3D 10, (1, 2, 5)…

A: Given:  a)   The equation of surface is   F(x, y, z) = xyz – 10 = 0   given point =1,2,5 On…

Q: 2. Find the area of the surface generated by revolving the given curve about the y -axis. (a)…

A: The surface area of the curve is given by

Q: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 7) = 4, fi(3, 7) = 2, f2(3, 7) i) Find g1…

A: The answer is given below: Correct answer is 2nd option and explana6 is given in step 2

Q: 8. Find the areas of the surfaces generated by revolving the curves: (a) x=2/4-y, 0sys15/4 about the…

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Q: Consider the surface given z = f(x, y) = e*#v. Then, af 1. af 2. dy 3. The equation of the tangent…

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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: x? y? The equation of the tangent plane to the surface z? 16 -1=0 at the point (4,3, – V3) is 9. O…

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Q: Consider the surface z = 4x2 + y? + 1. An equation for the tangent plane to this surface at the…

A: Let fx,y=z. Differentiate the function f(x,y) partially with respect to x and y, to find fx and fy .…

Q: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 7) = 4, fi(3, 7) = 2, f2(3, 7) i) Find g1…

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Q: 7 sin(æ), æ = T, I = 27 and The region R in the first quadrant of the xy-plane is bounded by the…

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Q: u' cos u?, r? EXAMPLE 6.6.3 For a surface of revolution defined by x u sin u?, x3 = f (u'), where f…

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Q: Let z = g(r, y) = f(3 cos(ry), y + e=y) provided that f(3, 5) = 8, fi(3, 5) = 2, f2(3, 5) = 3. i)…

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Q: Solve the problem. Find the equation for the tangent plane to the surface z = In(10x²+ 3y² + 1) at…

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Q: 14. Let II be the plane tangent to the implicit surface x? + y° – e*+2y = 4 + x sin(z) at the point…

A: According to question given that implicit surface x2+y3-ex+2y=4+xsin(z)Point are=(-2,1,0 )

Q: The surface area of the surface generated by revolving y 1-x? for 0Sr<1 about the x-axis is S=…

A: Rule- If the curve y=f(x), a≤x≤b is rotated about the x−axis, then the surface area is given by

Q: Let z = g(x, y) = f(3 cos(xy), y + e=") provided that f(3, 5) = 6, f1(3,5) = 2, f2(3, 5) = 6. i)…

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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: the surface area of a .17 rotating the curve y = x power 3 around the x - axis between the points…

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Q: g(x, y) = f(3 cos(xy), y + e#¥) provided that f(3, 6) = 6, f1(3, 6) = 2, f2(3, 6) = 5. %3D i) Find…

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Q: 3) Consider the curve C which is the intersection of the surfaces shown in the attached figure. If…

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Q: 11. Given f(z, y) = -r² - 4y?. (a) Sketch the surface f. (b) Determine the equation of the tangent…

A: We have a bivariate function f(x,y) = -x2 - 4y2

Q: ane for the level surface f(x,y,z) = 4x2 + cos (3y) + In (5z) = c %3D O.500z - 44 518

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Q: Find the tangential and normal components of acceleration at any time t of a particle whose position…

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

Q: Let z = g(z, y) = f(3 cos(ry), y + e=") provided that f(3, 5) = 5, fi(3, 5) = 2. f2(3, 5) = 5. i)…

A: It is given that the function z=g(x,y)=f(3cos(xy),y+exy). f3,5=5, f13,5=2,  f23,5=5 To find: i)…