What is the maximum value for a sinusoidal function having a midline y = 3 and a minimum at -1? (A) 1 (B) (C) 4 (D) 7

Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

Q: Determine the orthogonal trajectories of the hyperbola 3xy= 5 at the point (2, 5/6). Sketch the…

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Q: Use Green's theorem to calculate §. -y² dx + xy dy where C is the vertex triangle (1,3), (4,0) and…

A: Consider the given integral. I=∮c-y2dx+xydy The green theorem is defined as, ∮cPdx+Qdy=∬R∂Q∂y−∂P∂x…

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 21, (1, 4,…

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Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 ≤ t ≤ 2π, closest to the point (3/4, 0).…

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Q: 1. The temperature at the point (r, y) on an unevenly heated plate is given by T = f(r, y) = 100+…

A: Given f=100+5x2+15x+10y2gradient of f∇f=∂f∂xi+∂f∂yj     =10x+15i+20yjAt (2, 1)∇f=10x+15i+20yj…

Q: A heat-seeking particle is located at the point (2, −3) on a metal plate whose temperature at (x, y)…

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Q: 2. Find the coordinate of the points on the cardioid r=1- cose at which there is a horizontal…

A: We are given the polar curve: r = 1- cosθ use formula:         x=r cosθy=r sinθ then,  dxdθ=-sinθ+2…

Q: 6. Find the equation of the tangent plane to the surface: ==√√4-x²-2y², at (1,-1, 1)

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Q: Find all points on the ellipse x2 - xy + y2 = 1 at which the tangent line is horizontal.

A: The given equation of ellipse is,

Q: FInd a so that the curve y = x3+ ax2+ 44 will have a relative extrema at (2,5). Find other extrema…

A: The given curve is y=x3+ax2+44. Since the curve has a relative extrema at (2,5), x=2 is a critical…

Q: At what time t does the speed of a particle moving in 3-space with position function r(t) = ti+tj+…

A: To find the time at which the speed of the partial is minimum. Note that, the velocity is the time…

Q: 1. Give an equation of the tangent plane to the surface z= In(4y – x) at the point (3,1,0).

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Q: Find an equation of a generating curve given the equation of its surface of revolution. x2 + y2 − 2z…

A: Given equation of surface of revolution is, x2+y2-2z=0

Q: Tangent to the parabola z = x² + 3y² , x = 1 , at point ( 1, 2, 13

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

Q: 2/6 Consider the upper half of the ellipsoid f(x.y) = 1--n and the point P-- 3 on the level curve…

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Q: (7.5.0)- Find an equation of the tangent plane to the surface of z = sin(x – 2y) at the point %3D

A: Given F(x, y, z)=z-sin(x-2y) ∂∂xF(x, y, z)=∂∂x(z-sin(x-2y))=-cos(x-2y)∂∂yF(x, y,…

Q: Jategrate h (x.y) = (x+y)i+(-x)j over the closed curve that begins at (-1, 0), goes along the x-axis…

A: we will use green theorem here to solve this question

Q: Find an equation of the tangent plane to the surface 9x2 + y2 + 4z2 = 25, at the given point (0, −3,…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: 6. Find an equation of the tangent plane to the surface z = y² – x² at the point (-4, 5, 9).

A: Recall: Equation of the tangent plane to the surface z=f(x,y)  at (x0,y0,z0) is        fxx-x0 +…

Q: 5.) What can you conclude when dx is changing from negative to positive? A) fis at a local minimum…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find the minimum distance from the parabola x – y = 0 to the point (0, 3). Minimum distance = %3!

A: At P(x,y), the point of shortest distance the slope of the line from P to (0,3) must be…

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 <=t<= 2pai closest to the point (3/4,…

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Q: Find the derivative dydx of the hyperbolic spiral r=aθ.

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Q: 6. What can you conclude when dy is changing dx from positive to negative? A) fis at a local minimum…

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Q: Write an equation in general form of the tangent plane to the surface x^2+siny + z^3 = −4 at the…

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Q: 1. Find an equation of the tangent plane to the surface of z = sin(x - 2y) at the point (7,2,0).

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Q: . Use the second-derivative test for local extrema (: extrema for the function. Identify whether the…

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Q: Car B is b=100 miles directly east of car A and begins moving north at u=50 miles per hour. At the…

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Q: An equation for the tangent plane to the surface z + 3 = xy cos (2) at the point (3, 1, 0) is:

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Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: Find the minimum distance from the parabola x − y2 = 0 to the point (0,3) Minimum distance =

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z3 бх2 + у2 - 7у,…

A: Solved below...

Q: Determine the surface of revolution if the arc y^3 + y = x^2 + 6x on the interval [−5, −1] is…

A: The curve will appear like this

Q: Explain why a cubic Bézier curve is completely determined by x(0), x (0), х(1), and x'(1).

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Q: 4. Find the equation of the tangent plane to the surface ey + In(xz) – evz = 0 at the point (1,0,…

A: Given:

Q: What is the moment of inertia of this area about the line y = -10 ?

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Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: In what directjon from the point ( 1, 3, 2 ) is the directional derivative of 6 = 2 xz-y a maximum ?…

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Q: 22 2 Find the equation of the tangent plane to the level surface xy*z? (– 1, – 1, – 2) = 4 at the…

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Q: Determine the location of a point (x, y, z) that satisfies the condition xyz > 0

A: In four of the eight octants xyz>0 1) x>0, y<0, z<0 (2) x<0, y>0, z<0 (3)…

Q: What do you mean by asymptotically stable for autonomous equations ?

A: Given: asymptotically stale for autonomous equation A critical point x∘ of an autonomous system is…

Q: 1. Tangent to the parabola z = x + 3y?, x = 1, at point (1,2, 13

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Q: Pls help ASAP

A: Solve the following

Q: A heat-seeking particle is located at the point (2, −2) on a metal plate whose temperature at (x,y)…

A:

Q: Find the points on the ellipse 2x +y 1 where f(x,y)= xy has its extreme values. %3D

A: Solution:- Here we have to find the extreme value of  f(x,y)=xy subject to constraint…

Q: 1)Determine the equation of the tangent line to the intersection of the surfaces x²-y=0 and y+z²=16…

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Q: So x, = c,e +c,e", and x, = 3c,e" +c,e" Sketch the trajectories in phase plane 2 -2 -2 Comment

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Q: Find the tangent lines as directed. To the ellipse x²+2y²=9 perpendicular to the line 4x-y=6

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