4. Consider the cone z = x² + y?. (a) Show that the tangent plane to this surface at any point (xo, Yo, zo) # (0, 0, 0) exists and passes through the origin. (b) Explain why the point (0,0,0) was excluded.

Q: ) Find symmetric equations for the tangent line to the graph of f(r, y) = at (1, 2, 2) in the plane…

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Q: Find the point where the tangent line to the curve 7(?) = (V? +3,ln(?² +3),t) at (2, In 4,1) 5. %3D…

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Q: 1. Let S be the surface generated by the curve +y+4= 0 when it is revolved about the z-axis. (a)…

A: y = x2 - 4 (a) we choose x, θ as perameter = (x, - (x2 + 4) cos θ, -(x2 +4) sin θ)   (b) dr→dx= (1,…

Q: (4) Find the points Po = (xo, Yo, 2o) on the sphere x? + y? + z² = 9 so that the tangent plane to…

A: Topic- equation of tangent in 3D

Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

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Q: Ř(u, v) = (u², v – 2u, u + v²)

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Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

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Q: Find the equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

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Q: Find the equation of the plane tangent to the surface z = 3x² + y² at (1, 1, 4).

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Q: Let S denote the cone x? + 4y? = z². (a) Find an equation for the plane tangent to S at the point…

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Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

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Q: 8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at…

A: This is problem of vector calculus.

Q: Where does the plane tangent to z = At z = 5exy at (7, 7, 5) meet the z-axis?

A: We find equation of tangent plane to z=5e^(x-y) at (7,7,5)

Q: e'y x+y² a) Find the equation of the tangent plane to the surface at the point P(0, -2). Present…

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Q: Find the equation of the tangent plane to the sphere x² + y2 + z² = 1 at the point (1/ V3, 1/V3, 1/…

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Q: Solve the differential equation xy' - 3y = 2x° In x. The solution is y = (Type an expression.)

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Q: Find the equation of the tangent plane to the given surface at the point P. x2 + y2 + z2 = 9, P =…

A: Concept Used:- For an implicitly defined function f(x, y, z)=0 The equation of the tangent plane to…

Q: Let P* be a refinement of a partition, P. Show U(P*, f, a) < U(P, f, a)

A: Upper Riemann sum and lower Riemann sum are the very important parts of Riemann integration. Lower…

Q: 4. Consider the parametric curve x = cost, y = sin cost, te [-T, π]. (a) Show that (0,0) is a point…

A: Consider the parametric curve given by  and , where  belongs to .a) To show that  is a point of…

Q: The equation of the tangent plane to the surface ye+z 0 at the point (0,-1,1) is az+by+cz 1. Which…

A: If  F(x, y,z)=0 is a three variable real valued function and generates the surface S, then the…