4. Setup an integral expression for the perimeter of the ellipse x² 3 Hint ds = x' (t)² + y' (t)² dt = √/₁ + (f'(z)) ² dz [² a + y² = 1 1 = = ds

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: dy −2r — 9 (a) Show that = dx x + 2y (b) Find the two points where the curve given by the original…

A: Given- Consider the equation x2 + xy + y2 = 19.  To find-  Show that dydx = -2x - yx + 2y.  Find…

Q: (xy^2- y^2+x-1)dx + (x^2y-2xy + x ^2+2y-2x+2)dy = 0 Start by using seperable equations.

A: given a differential equation,here need to solve this differential equation by seperation of the…

Q: x+y y² +1 #2) (x + tany)dx +- -dy = 0.

A: here we have to solve the differential equation.

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: a) Find dy if y² + x²y² = 1+x^y use implicit differentiation b) If x² + y² = 6. Find y' in term OF…

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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: Consider 2a – 3y² = 8

A: Differentiate wrt x