th from the Parameter equation (use the Parameter Equation formula (z(t)=x(t) + y(t)i ). Z(t) = t+3ti (1< t < 4)

Q: 2.22. Plot the curve Yk+1 = Y% – 2yk +2 and analyze the stability of any fixed points. Show that the…

A:

Q: X () = (:)- Find the solution that satisfies the initial condition %3D

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Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: In Exercises 1-6 use variation of parameters to find a particular solution. y"4ysin 2x sec2 2x 2.

A: Result used:

Q: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

Q: 2. Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated…

A: y=ax3+bx2+cx+d-1Critical points 1,0-2,27We know that at critical point dydx=0 or does not exist…

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: Find real-valued closed formulas for the trajectory x(t + 1) = Ax(t), where [-0.8 A = -0.6 -0.8] 0.6…

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Q: Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated condition.…

A: Given curve is y=ax3+bx2+cx+d        (1) and critical points are (1, 0) and (-2, 27) We have to find…

Q: c) Find the minimum distance from the point (4,0,6) to the plane x- y +2 = 3

A: The solution is given below. .

Q: A heat-seeking particle is located at the point P(6,4) on a metal plate with temperature at (x, y)…

A: Given, a heat seeking particle is located at the point P(6, 4). The temperature function is given…

Q: Find the point(s) on x = 3 - y that are closest to point A = (1,0).

A: Given: Curve x=3-y2 and a point A(1,0).

Q: b) Find the point on the curve y Vr that is closest to the point (7,0).

A: Find the point to the curve y=(x)^(1/2) that is closest to the point (7,0)

Q: Find the orthogonal trajectory of the family of curves x² + y² Cx

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Q: show that the solution y(t)=e^2tsin(t) is linearly independant.

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Q: Find equations of the two lines that are tangent to the circle x2 + y2 = 1 and pass through the…

A: Given equation of circle,  x2 + y2 = 1  To find the tangents ti the circle and passing through (0,…

Q: FInd c so that the curve y = x3+ cx2+67 will have a relative extrema at (2,5). Find other extreama…

A: Consider the equation of the curve, y=x3+cx2+67 Solve for the stationary points as,…

Q: (6) Find the orthogonal trajectories of the family of curves y = ax? + 4ax + 4a, where a being…

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Q: Eliminate the parameter to obtain an equation in x and y: x=-2cos2t, y=-2sin2t

A: x=-2cos2t y=-2sin2t using trigonometric property,               sin2t+cos2t=1

Q: A parabola has the equation y^2 = -4ax. Determine the slope of the orthogonal trajectories. 2x/y O…

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Q: Find the orthogonal trajectory to the family of curves: y(x²+1) = Cx

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Q: Write dOWn the second order rainary aiIfere equation y" + 2y' + y? = 4 as the fist order system,…

A: Given , second order ordinary differential equation ,      Let  then from (1) , Now , First order…

Q: -Obtain the Cartesian equation of the curve by eliminating the parameter. 14) x = t - 3, y = t2 + 5…

A: To obtain the Cartesian equation of the given curve.

Q: The line that is normal to the curve x + 2xy - 3y = 0 at (4,4) intersects the curve at what other…

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Q: Let y = v2x. Determine the point (x, y) that is closest to the point (5, 0). That is, deteremine the…

A: find the minimum distance from a point

Q: 1. Find the shortest distance from the point (1,0, –2) to the plane x+2y+z = 4.

A: We have to find shortest distance

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Given y=x3+cx2+d

Q: Find the equation of the curve, in the XY plane, that passes through the point (2, 2) and is such…

A: Differential equation

Q: a) Find the extreme values of f(x, y) = x' + y' - 3xy +1 by using the Second Derivatives Test. b)…

A:

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: The equation of the curve in the tx-plane which passes through the point (2,3), and has, at every…

A: In this question, slope of curve and point is given and we have to find out equation of cuve.

Q: Determine the coefficient a, b ,c and d so that the cruve will satisfy the stipulated condition.…

A:

Q: (c) Given that y = x4 – 8x²

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Q: 5. Determine the coefficients a, b, c, and d so that the curve will satisfy the stipulated…

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Q: Find the orthogonal trajectory of the curve x^2 + y^2 = 2 ln cx

A: Given query is to find the orthogonal trajectory of the curve.

Q: Determine the location of a point (x, y, z) that satisfies the condition(s). xy &gt; 0, z = −3

A: Here Our Aim is to determine the location of a point (x,y,z) that satisfiesthe condition(s):→…

Q: Riemann sits on the line normal to the curve y=x2 -3x+2 at x = 1

A: Given           y=x²-3x+2 and x=1  Slope of the curve is given by =dy/dx

Q: Find the equation of the xy-trace, the equation of the xz-trace and the equation of the yz-trace of…

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Q: Find all equilibrium points and determine their types when C =1. i, = x2 i, = -bx, +1+ c(-1+…

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Q: A curve C has equation y =x2lnx- 2x +5, x > 0. %3D For which values of x, the curve C is convex?

A: The equation of the given curve is  y=13x2 ln x-2x+5 , x&gt;0 For the curve to be convex its second…

Q: find the location of a point xyz that satisfies the condition I) xy<0, z=3 ii) |x|<2

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Q: Find the orthogonal trajectory of the curve x^2-y^2+2Cx=0

A: Given equation is: x2-y2+2Cx=0 Differentiating with respect to x we get, 2x-2yy'+2C=0⇒x-yy'+C=0…

Q: 2.22. Plot the curve Yk+1 = y% – 2yk + 2 and analyze the stability of any fixed points. Show that…

A: Given, yk+1=yk2-2yk+2....(1) We can write the given equation as, fx=x2-2x+2.....(2) Now, finding the…

Q: Consider the path equation r = (cos(t), t) = cos(t)ˆx + tyˆ.    For which time value t ∈ (3π/2,…

A: The radius of curvature at each point of the curve, ρ:ℝ→ℝ, is given by:ρ=r'3r'2r"2-r'·r"2…

Q: i. Discuss and sketch the curve x² + 6 x = -8 y – 25 ii. For the curve y = x3 – 6 x2 + 10 - (a) Find…

A: (i) Given equation of the curve is x2+6x=-8y-25 This can be rewritten as,…

Q: Ax, y) = 6xy %3D 2.

A: The local maximum and minimum values and saddle points are given as follows :

Q: 3. When origin shifted to the point (2,3), the transformed equation of the curve is x2 + 3xy – 2y2 +…

A: Shifted origin is 2,3. Transformed equation is x2+3xy-2y2+17x-17y-11=0. Replace x with x-2 and y…