Need help with the following problems: 1. Solve this differential equation: e^t (dy/dt) = y^2, y(0) = -1/4

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Q: Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t),y = 2…

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Q: x = 7 te', y = (t + 1)e', 0stsi Set up an integral that represents the area of the surface obtained…

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Q: 2. Given the parametric equations: x = t + sin t,y = t- cost, findand

A: Solution...

Q: #3. Find parametric equations for the tangent line to thể curve with parametric equations x = (sin…

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Q: QI: Find the area between x =2y2 + 3 and x = y2. %3D

A: x=-2y2+3x = y2

Q: 9. Given the parametric equations x = et and y = te-t, vt. dy (a) Find dx (b) Find dx2 d?y (c) For…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given To find parametric equations for the tangent line to the curve with the given parametric…

Q: baseball is hit at 120 ft/sec from the ground at a 300 angle to the horizontal from a height of 3…

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Q: (a) Let f(x, y) = sin(y?). Compute fry and fyr and show that they are equal to each other. (b) Let…

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Q: dy (ii) Find dx? for the parametric equations x = t+ sin t, y= 1+cost

A: • This problem can be solved by using Chain rule as explained in step 2.

Q: Which is a parametric equation for the curve 25 = (x +7) + (y+ A. c(t) = (5 cos(t) – 5, 5 sin(t) –…

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Q: x=t3/3  y=t2/2     0<t<1  resolve the parametric equation

A: Given that , x=t3/3  y=t2/2     0&lt;t&lt;1  Resolve the given parametric equation.

Q: [x(t) = 3t² – 3 v(t) = 2t +1 Find the slope of the tangent to the parametric equations at t=1.

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Q: - 1. Evaluate the x for parametric equations x = 3t² – 6t a y = 3t³ + 3t with respect to the…

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