Find the differential eqn. of the ff. family of curves: a.) Straight lines with slope half the value of the x-intercept b.) Circles with center on the y-axis c.) Circles with center on the line y = x, and passing through the origin

Q: Find the tangent plane to the equation z = 6e* – 2y at the point (4,8,6) - II

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Q: Find an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

Q: Find the equation of the tangent plane to the graph of G(u, w) = sin (uw) at the point (r, ).

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Q: Find an equation of the tangent plane to the surface g(x, y) = x2 + y2, at the given point (1, −1,…

A: We have given the surface; g(x, y) = x2 + y2 and the point (1, −1, 2)

Q: Find the length of the subtangent and sub-normal at a point of the curve y= bsin(x/a)

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y?, (6,…

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Q: Find an equation of the tangent plane and a normal line to the surface z = In Vx2 + y2 at the point…

A: Given that: z=lnx2+y2

Q: 3. Find the equation of the tangent plane and normal to the surface z =x? +y? + 4 at point (1, -1,…

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Q: Use the IVT to prove that the curves y = x2 and y = cos x intersect.

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y², (12,…

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Q: Find the point(s) on the surface z = 5xy, at which the tangent plane is horizontal.

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Q: Find an equation for the tangent plane to the surface z = 4xy® + sin(rx) at the point (1, 1, 4)

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Q: Find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in…

A: Let's find.

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2 + y²,…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan Y, (6, 0,…

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Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = cos t, y = tan t

A: Given that, x=cost, y=tant We have to eliminate the t and express curve in the form y=f(x). As we…

Q: Find the slo pe of the Para bola y=X at the Point PC2,4).write an equation for the tangent to the…

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Q: Find the speed of the cycloid c(t) = (4t − 4 sin t, 4 − 4 cost) atpoints where the tangent line is…

A: Given: c(t)=4t-4sin(t), 4-4cos(t)

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan , (7,0, 0)

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In Vx2+ y², (3,…

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Q: Find an equation of the tangent plane to: 3x +y = z at P(-1,1,-2) %3D

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Q: 13. Find an equation for the tangent plane and the normal line to the surface x? + 2y? - 3z? = 3, at…

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Q: Find the tangent plane to the surface z = 9 – x* – y? at the point (1, -3, –1).

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Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In√√x² + y2, (3,…

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Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)

A: Given; z=2ycos(5x-4y) at the point (4,5,10)

Q: (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? +…

A: Conicoid given is- Ax2+By2+cz2=1 at the point (α,β,γ) We have to obtain the equation of the tangent…

Q: x² = y + 3y.

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Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. 2z…

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Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan y/x ,…

A: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan(y/x).…

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In V x2 + y², (6,…

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Q: Find an equation of the tangent plane to the surface at the give h(x, y) = In √x² + y², (12, 16, In…

A: we have to find tangent plane

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (4, 0,…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (1, 0,…

A: This question is based on finding equation of tangent plane of function having two variables at a…

Q: If x = 8cos3theta and y = 8sin3theta, find the total length of the curve swept out by the point…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = = arctan 2, (9,…

A: Follow the procedure given below.

Q: Find an equation for the tangent plane to the surface z +4 = ry" cos(2) at the point (4, 1, 0).

A: Use the partial differentiation for finding the tangent plane.

Q: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given surface 1)…

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Q: Sketch the cardioid r = 3 cos 0 and find the coordinates of the points on the cardioid where the…

A: Given polar equation is r=3cosθ

Q: Find an equation of the tangent plane to the surface z = y? - x² at the point (-4,5,9).

A: Finding partial derivatives with respect to x and y for finding plane equation.

Q: Find the diffrential equation of for each of the curves determined by the condition that at each…

A: length of subtangent =ydydx

Q: Find an equation of the tangent plane to the surface z = √(9 − x2 − y2), at the given point (1, 2,…

A: The surface given is Fx,y,z=√(9 -x2 -y2) -z =0. The derivative of the surface coordinates with…

Q: Find an equation for the tangent plane and the normal line to the surface x? + 2y? – 3z² = 3, at the…

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

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Q: where c is a constant, then prove that the foot of perpendicular from the origin upon the straight…

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