(2² + y² – 1)³ – x²y3 = 0, 2- Given the curve dy find dx -2 2

Q: Given dy (1 + 3 k). dx 13 2 What is the value of k such that y is parallel to the curve y = 3x +1 at…

A: Given,            dydx=2131+52x-32-34k            The curve is y=3x+1 at x=1.To find : The value of…

Q: Find the equation of the tangent line to the parametric curve. x = t1/2 y = t3/2 at t = 1. Also…

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Q: A particle moves along the curve y=x3-x. If vx = 2 ft/sec and ax= -3 ft/sec2 as the particle passes…

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Q: Given =흙(1+ 들교 -볼 - 클시. dy 2 3 (1+ x – dx 2 What is the value of k such that y is parallel to the…

A: topic- slope of the curve

Q: 3. (16х + 5у)dx + (3x + y)dy %3D0 the curve to pass through the point (1, –3)

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Q: differenetiate parametrically to find dy/dx in terms of t:  x=1/t+1 , y=2t^2-4

A: please use according to form i did solved two equation because your question is not write clear that…

Q: The position of a particle in the xy-plane at time t is r(t) = (t+2) i+ (t- + 3) j Find an equation…

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Q: Consider the curve defined by x2y + 3x + y2 = 38. a. Find dy/dx dy dx .   b. Find an equation of…

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: 18. The length of the curve y = r* from r = 0 to r = 2 is | V1+2® VItz® dz B. | V1+3x2 dx A. C. D.…

A: Question 18 is solved. Solving more questions are against the policy of bartalby. In question 18 ,…

Q: Can you please solve these two sub problems and show all of the steps and say the correct letter

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: (16x + 5y)dx + (3x + y)dy = 0 the curve to pass through the point (1,–3) %3D

A: The solution of the problem is given in the next steps.

Q: Which of the following gives the length of the curve y = Vx over the closed interval [1,4]? (A) - dx…

A: Explanation and solutions is given below....

Q: Cvaluate (xy) s ds where C is the curve y = x², for 0 < x < 2.

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Q: Find dy/dx and d²y/dx² at t = 2 for the parametric curve x = ½t², y = ⅓t ³.

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Q: 1. y = 2t2 – 7t3, x = 9t – t5

A: dy/dx and d2y/dx2  are find in next step dy/dx = (dy/dt) /(dx/dt)

Q: Find dy dx2 Q2 when t = 1 if given the parametric functions as below, x = 3e5t y = te-5t

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Q: 1. Calculate the derivative dy/dx for the plane curve defined by the equations…

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Q: 7. a. Find the points on the curve x = 3(t2 – 3), y = t³ – 3t where the tangent is horizontal or…

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Q: I need help with 1a)

A: straight line becomes y=x

Q: dy in terms of t: Differentiate parametrically to find dx y= 2t2 +4 t - 1 X = A [4t(t – 1)²] В…

A: Given :x=1t-1y=2t2+4

Q: dy 14ya® dx such that y(0) = 6. y(x) =

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Q: (x = t³ + 7 y = t5 – 3t d²y calculate for a function given parametrically dx?

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Q: For the curve y = f(x) = x², 0 ≤ x ≤ 2, its length is 2 L = 1+ dy dx dx =

A: Given curve y=f(x)=x2,0≤x≤2 The objective is to find the length of the curve.

Q: 20. The curve 2x2y+ y 8x +1 passes through (4, 1). Using the tangent line to the curve at the point…

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Q: dx 6 when x=1, what is dt dy If y=x is expressed with parametric equations such that dt

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: dy of the curve yln x + 5x² + y' = 13 at the point (1,2) dx b) Find

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Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: 1. If F(x, y) = (3+2xy)i + (x² – 3y²)j. Evaluate F. dr, where C is the curve given by r(t) = e'…

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Q: Find 4 at the point t = 5. dy dx c(t) = (t^, t³ – 3) dy dx (at t = 5) = ||

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Q: Find the equation of the tangent line to the parametric curve. x = t1/2 y = t2/3 at t = 1. Also…

A: The curve is defined by the parametric equations as x(t) = t1/2 and y(t) = t 2/3   Apply the chain…

Q: dy in terms of t: Differentiate parametrically to find dx 1 y = +2 t+1

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Q: (A) Evaluate" [(x² + y)dx + (x + 1) 1+ along the path ABCA shown in figure C(0,3) A(0,1) x=3sint…

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Q: [&+2y)dx +(x² - 3y°)dy (3+2 4. Evaluate where C is any smooth curve from the point A (1, 0) to the…

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Q: 7. Find fSp(x - y)*dx dy, where D is Figure 17.2.13. y A シ=V ソ=2-

A: Answer is 64/35

Q: Q7// Find tangent and normal equations of the curve x³ + y3 – 9xy = 0 at points (4,2) and (2,4).

A: The slope of a curve at the point (x1, y1 ) is given by;…

Q: d²y + y = 0 cos x 2 dy a) Show that if y then + dx² x dx dy b) Find dx given y = sin vx c) Determine…

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Q: 8. Find parametric equations for the tangent line to the curve r(t) = (t² +3t +2, e' cost, In(t +1)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Q4] Find the equation of the tangent plane and normal line to the surface z + 8 = x ey cos z at…

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Q: Find [(dy)/(dx)] if the curve is defined by 7 x² e7 Y + 6 y2 e2 x = 16. %3D [(dy)/(dx)]

A: Given:     7x2 e7y + 6y2e2x = 16

Q: Find dy/dx and d2y/dx2 at the given point without eliminating the parameter. x=1/2t2+9  y=1/3t3+4t,…

A: We have, x=12t2+9, y=13t3+4t, and t=2 Now, differentiating x=12t2+9 with respect to t, we get the…

Q: 2. Find for the curve dx x²y3 – 2xy = 6x² + 2y³ + 1 -

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Q: -38x^8+10x^76y+y^9=-27, find the dy/dx. Now find the tangent line to the curve (1,1). Write in…

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Q: Find dy/dx and d62y/dx62 at the given point without eliminating the parameter. x=1/2t^2+9…

A: Given parametric equations are: x = 1/2t2 + 9 y = 1/3t3 + 4t Differentiating x with respect to t we…

Q: dy lat dy %3D dx dt 5) Find the equation of the line tangent to the curve using the fact that: For…

A: Given equation is Differentiating with respect to , we get   Now, Now, t=e corresponds to given…

Q: 1. Calculate the derivative dy/dx for the plane curve defined by the equations: x(t)=t²-4t,…

A: Given that: x=t2-4ty=2t3-6t

Q: xe" dx+x²ydy Compute e'dr+r'ydy along the curve C: * = 31, y =t² ,0<ISI

A: Topic: application of integration

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.