- z²) – 2x + 30y = 0 da? What is the larger root from the indicial equation

Q: Show that the equation of the tangent line to the hyperbola                        x2/a2 − y2/b2 = 1…

A: Given Data The equation of the hyperbola is x²/ a²- y²/ b²=1. The points are (x0,y0).…

Q: At what point does the normal to y = 2 + 2x + 2x² at (1,6) intersect the parabola a second time?

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Q: For the hyperbolic PDE u, +bu, =0 a) Find the finite difference equation, using forward for u, and…

A: Given: The given hyperbolic PDE  ux + buy = 0 a) To find the finite difference equation, by using…

Q: Q3// B Verify that dv3p'sin Ddpd@d owhen using spherical coordinate

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Q: What is dyldx at the point (1,2) of xy^2 + 2xy 8 ?

A: The given equation is: xy2+2xy=8...(1)

Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x) %3D and C is the curve in the third quadrant…

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Q: Match the ellipsoids shown in the figure above with t 1) x2 + 4y + 4z? = 16 2) 4x2 + y +4z? = 16 3)…

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Q: At what points does the curve  r(t) = ti + (5t − t2)k  intersect the paraboloid  z = x2 + y2

A: We have to find the intersection point

Q: state whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: Rearrange the equation, 3x2-7y2=z by dividing both sides by 21 and obtain x27-y23=z21. The general…

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

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Q: Show that the parabolas $r=c /(1+\cos \theta)$ and $r=d /(1-\cos \theta)$ intersect at right angles.

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Q: Find the tangent plane to the equation z = 4x2 + 2y? + 5y at the pc

A: Here we have to find the equation of the tangent plane on the curve z=-4x2+2y2+5y at the point…

Q: Evaluate [. 2y² + 4z² ds, where o is the first octant portion of a cone z = x² + y2 with height of…

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Q: whose x-coordinates are equally ine with parabolic runout conner

A: Given as.     python code :

Q: ind the equations of the tangent line to the ellipse x² + 4y² + z² = 9, x = 2 at the point (2, -1,…

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Q: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

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Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

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Q: Sketch the graph of the cylinder given by 4x2 + 9y2 = 36. show solution

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Q: I need a 3d sketch of the equation  Z=x+xsiny+xy

A: z=x+xsiny+xy

Q: B.2. Express to its standard form, determine the center, radius ar 10. x² + y? + 10x – 14y + 58 = 0…

A: # We are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: Find an equation for the tangent plane to the surface 2° – ay? = 0 at the point (27, 1, 3).

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Q: (b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at the point (1,…

A: We have to find the equation of the tangent plane to the hyperboloid x² + 3y² − 3z² = 1 at the point…

Q: Find an equation of the tangent plane to the surface 3x? + 2xy – 4z2 + 2x – 3y = 0 at the point P(0,…

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Q: (2) Find the Ualue of the constant m while the Curl of Foaoy,z) = (mxy- 2) Ĉ +cm-2)x)+(1-m)x2° Â is…

A: Please see the answer in step 2

Q: 6. Prove (by plot) the equation (x²+y²=16) is the circle in 2D , and cylindrical in 3D.

A: We will answer the first question since we don't answer multiple questions at a time. Please…

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

Q: Classify the equation yʻuxx + 2xyuxy + 2x-uyy + xux = 0, and reduce it to canonical form.

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Q: 4 du + 3, du -o is dassified as Jhe P.O E dx² © Hyperbotic Elliptic Parabolic there of

A: 4∂2u∂x2+3∂2u∂x∂y=0

Q: Show that the equation of the tangent line to the hyperbola x2/a2 − y2/b2 = 1 at (x0, y0) is x0x/a2…

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Q: Find the best quadratic approximation, Q(r, y) of V9 – 6x – 4y for (r, y) (0,0). near

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Q: Find Dy 2 y of the following parame equations: x = t2 - 2t +1 y= 2t2 - 4t3

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Q: Find the equation for the tangent plane to the surface z= In (7x + 10y + 1) at the point (0,0,0).

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Q: Find symmetric equations for the tangent line to the curve of intersection of the paraboloid zx +y…

A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

Q: Find the tangent plane to the equation z 4e- 4y at the point (8, 16, 4)

A: Let x0,y0,z0=8,16,4 be a point on the given surface. Then, the equation of tangent is…

Q: Find the equation of the tangent plane to the surface 9x +36y +4z? = 108 at the point (-2,1,-3).…

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Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

Q: Evaluate (x - iy) dz along (a) the parabola y = 2r? from (1, 2) to (2, 8),

A: In the given problem we have to evaluate  ∫C(x2-iy2)dz  along the parabola  y=2x2 from (1,2) to (2,…

Q: The tangent plane to the elliptic paraboloid z = -2x - 7y? at the point (-3, -4) is

A: Consider the provided question, The equation of the tangent plane to the elliptic paraboloid at the…

Q: b) Find the points on the curve 2 17x + 12xy + 8y“ = 100| that are farthest away from the origin…

A: Substitute x = rcosθ and y= rsinθ

Q: Consider the parametric equations: x = 2t2, y =43t3. Find d2ydx2at the point t=18 without…

A: Given parametric equations are x=2t2 and y=43t3. To find d2ydx2 at the point t=18 without…

Q: By means of Lagrange's formula, prove that 1 Yo = - 1 - [2 (y₁+y_₁). (Y3 - y₁) 2 -Y₁) - 2 (Y-₁-y-3)…

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Q: 4. Classify the type of the equation as elliptic, parabolic or hyperbolic. Uxx xuy+xu 0 =

A: The given problem is to classify the given partial differential equation as elliptic, parabolic or…

Q: The indicial equation of (r – 1)?y" + (x³ – 1)y' + 2y = 0 at = 1 is :

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Q: 4. (i) Use the parametric equations of an ellipse, z = a cos (t) , y = bsin (t), 0 < t< 2r, to find…

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Q: Find a parametric function for the intersection of r – 3y + 4z = 0 and a? + y² = 9.

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Q: Ex6:compute 4Cメッッ) du where: 4(メy)4 メサ by using spherical coordinates system.

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Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

Q: Compute y ds over the part of the parabola y =2Px, for P > 0 starting at (0,0) at (2P,2P).

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Q: At which points does the curve r(t)=ti+(2t -t² )k intersect the paraboloid z = x² +y? ?

A: Given: r→t=ti^+2t-t2k^ and z=x2+y2

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.