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

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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 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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