Give a parametric representation for the path followed by a heat seeking particle placed at point P on a plate if the temperature field of the plate is given by T(5x). |Change (y' to y² ). T(x, y) = 64–x² – y P(4,2)

Q: Let h be a differentiable function of z obtained from the parametric equations z = f(t), y = 9(t).…

A: Option  1  is true .

Q: Find the points where the tangent is parallel to y=0. y=x*-8x°+22x2-24x+9 O E 0 (1,1),(2,2),(3,0) O…

A: Given: y=x4-8x3+22x2-24x+9 And y=0, represents the x-axis. The Power law: ddxxn=nxn-1

Q: ƏT ƏT and dr 3. Find of function T = x²y – xy³ + 2; x = r cos 0 and y=r sin 0

A: We have to find derivative

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: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

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Q: V= tan -¹ (y/x) verify vxx+vyy=0 or not

A: Given, V=tan-1yx     Verify Vxx+Vyy=0 or not

Q: Which of the following gives the length of the curve y x2 + 2x from x = 0 to x = 5 ? (x2 + 2x) dæ I…

A: Length of the given curve will be

Q: Draw a direction field (slope field) of y' = x. Use all 25 grid intersections. 2 1 2 X

A: Note: Slope fields allow us to analyze differential equations graphically. When an explicit solution…

Q: X- An ant is moving on the surface z = x² + xy + y² such that its - and y-coordinates satisfy cost,…

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Q: -1 (3). Let g(x, y) = e2y tan value of g does not change. - 2. Find a direction from the point (1,…

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Q: Determine when the following pairs of functions are linearly independent. (a) y1(t) = e"it; Y2(t) =…

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Q: Plot the slope field of y=x+y using slopes m = -3, -2,-1,0, 1, 2. Sketch integral curves for…

A: First we plot the slope field and then plot the curve .

Q: Let f(x, y, z) = x“y + z* and x = s³, y = st°, and z = s°t. (a) Calculate the primary derivatives ,…

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Q: Find the equation for the curve f (x) at the point (x, y) meet the following conditions dy / dx = 4x…

A: A curve is a function with equation of the form y=f(x). A differential equation is an equation in…

Q: Evaluate y dx + x dy along the curve y x² from (0,0) to (1, 1).

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Q: Evaluate I= √ (sinx+2y) dx + (6x+y)dy for the non closed path ABCD in the figure.

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Q: Function dy du dy du dx dx = (5x³ – 7x² + 2x – 3)*) _y = csc(x² – 3) y = 5x² – . y = V5x2 – 4 _y =…

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Q: Eliminate the constant: =c₁e²x+c₂e³ 3x

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Q: Consider y=(x2+1)2x a) find dy/dx b)Evaluate y'(1)

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Q: iv is analytic = -11..

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Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

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Q: 4) Find dy given: y (1-x)(1+ x )(1+ x³ )(1+x*) dx d'y given: y= (5x -3X7x+x) 5) Find dx

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Q: ) Find y as a function of x if x?y" + 2xy' – 42y = 0, y(1) = 5, y'(1) =-3. y =

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Q: Find y' and y". (x – y)3 = x – xy + 1

A: Topic :- Derivative

Q: 2. Y=12-36x, Y'co) = 5, 2. dx and yeo) =S. YCx) =?

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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: Find y as a function of a if y(1) = −2, y′(1) : = 4. y = x²y" + 9xy' + 16y = = x³,

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Q: 1- Find dB/dx for the follow ing functi'on a)- xy = Cot (xy) b- y Sim(hs =-メy %3D c)- y?cos () 2x+2y…

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Q: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…