4. a) Find the general solutions of the following differential equations. Express the general solution in y = f(x) whenever possible. dy x² = dx¯¯_y(1+x²) b) dQ dt =k(Q-70), k is any constant > 0

Q: 3. Find the slope of the tangent line of the following curves at 0= 1/3 r = 2 cos Ⓒ

A: We can solve this as follows:

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A: Solution below

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Q: f(x) = 1 X-3

A: f(x)=1x-3if f'(x)>0, than f(x) is increasing if f(x)<0, than f(x) is decreasing d dx(xn)=nxn-1…

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A: The graph is given

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A: (a) f(x)=5-8x1+2xd dx(ab)=bdadx-adbdxb2d dx(xn)=nxn-1

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A: We have to slove above question

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Q: so what is the answer for xi and f(xi)?

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Bernoulli Equations des 4 1/3 y²-³ y=x²y²²

A: y'-3xy=x4y13divide both side by y13

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A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

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A: f(u)=u3g(x)=4+9x2(f∘g)(x)=f(g(x))

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A: From the given graph we can conclude as