Solve the following initial-valued problems. y'=(y/x)+2,   y(1)=3

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A: We have to approximate  S=∑n=1∞ 2*(-1) n+1/n!      On expanding this series we get S= 2[1-1/2! +1/3!…

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Q: Let u = x + 7y and v = x - y. Subtracting v= x - y from u = x + 7y, we get y = Adding u =x + 7y and…

A: Given:      Let u=x+7y              v=x-y Subtracting v=x-y from u=x+7y, we get…

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A: Given :

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Q: (x=1² +3t – 1 + 3t – ; at t=-2. t-2 y = t² +1

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Q: x2 - 4x - 12 Find f'(x), f'"(x), and f8(x) for the function f(x) X+2 f'(x) = everywhere that f(x) is…

A: Given

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Q: x²– 9 ?

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Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

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Q: The most conveneient way to evaluate x² – 4 by substitution is to let x2 – 4 =y A True B False

A: On solving this we will get

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Q: a. Use the product rule to find the derivative of the given function. b. Find the derivative by…

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Q: Suppose a population function P(t) satisfies the following differential equation. P is measured in…

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Q: Find the arc length L of the graph of r(t). r() = r° i + 1 j+Vor k, 3 <t<7 L = i

A: Given problem:-

Q: Use the fundamental theorem of calculus to evaluate the following definite integral. | (3x2 + 9) dx…

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Q: An arithmetic sequence has first term a = 5 and common difference d = 8. How many terms of this…

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Q: Ise the function f and the given real number a to find (f-)'(a). (Hint: See Example 5. If an answer…

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Q: 21. Find af and of if f(x,4)= 3x" +2xy+ Sy , x= 4v? + Bn", and u 2v-w? Vour %3D 4= 2v-w? Vour av…

A: We have to check

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Q: A candy box is made from a piece of cardboard that measures 31 by 17 inches. Squares of equal size…

A: let the cut out square side be "x"length of cardboard is 31 inBreadth of cardboard is 17 inAfter…

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Q: (t) satisfies the following differential equation. P is measured in millions and t is in years

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Q: I having trouble following the part where they take the natural log of the limit and the…

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Q: Verify Green's Theorem by evaluating both integrals y2 dx + x² dy = dA ду for the given path. C:…

A: In this question we can verify the Green's Theorem . i.e, ∫C M dx +Ndy = ∫∫R ∂N∂x-∂M∂ydA .

Q: The particular solution that satisfies the differential equation and the initial condition of dy/dx…

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Q: Ty csc?y dy is equal to A —у сoty — coty dy - Scon dy у сoty coty dy с) -у соfу+ coty dy D) None E у…

A: Integrate by parts.

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Q: The point P(p, 1), where p > 0, lies on the curve x² + 2xy³ – 3y* = 0. a) Calculate the value of p.…

A: Since point , P(p,1) lies on the given curve, therefore this point will satisfy the curve .Using…

Q: Consider the initial value problem. y'' − y' = ex,              y(0)=0,   y'(0)=0 (a) Write the…

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Q: Find the volume of the solid that is bounded by the surfaces z = 152 - x2 - y?, z = 0, x = 0, y = 0…

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Q: 00 (n+7)! Does the series converge or diverge? 7!n!7" n= 1 Choose the correct answer below. O A. The…

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Q: A ladder of length 4v3 metres is resting on a wall. The wall makes a 60-degree angle with the…

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