3. (a). For a curve defined by an equation f(x), satisfy dy + (1 – 2x)y = 4x for x > 0 and - dx f(1) = 3(e2 – 1). Determine an equation for y = f(x). -

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A: We will find the required.

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Q: 4. Find the equation of a line tangent to f (x) = –x² – 4x at x = -1.

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Q: Find the equation(s) of the tangent line(s) to the graph of the curve y-x-12x through the point (1,…

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Q: (a) The curve y = 1/(1 + x²) is called a witch of Maria Agnesi. Find an equation of the tangent line…

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Q: 144y+312y+ 169y= 0. y(0) = 6. (0) = 6. %3D %3D

A: Let the given differential equation be, 144y''+312y'+169y=0 Assume the solution of the differential…

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Q: 3- find an equation for the line tangent to the graph h(t) = t³ + 3t, (1, 4) %3D

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Q: Write the equation of the tangent line to the curve y = x + 6x - 3 at (1,4).

A: Given,           The curve is y=x2+6x-3 and the point is 1,4.To find: The equation of the tangent…