3 Evaluate: ³₁²₁ ¹²[z³(x + y)³] dz dy dx -4 1

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Q: . Solve the following problem (a) Y'(t) = XY(t) + 1, (b) Y'(t) = \Y(t)+t, Y(0) = 1. Y(0) = 3.

A: In this question, we will solve the given linear first order differential equations.

Q: 2. Given the graphs of f(x) and g(x) as shown, find: ✓✓✓✓ a) f(g(0)) b) f(g(2)) 67. -20 -2-

A: f(g(0))=? f(g(2))=?

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A: This question can be solved using the concept of linear differential equation. Note: elna=a

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Q: v²dx + x(x + v) dv=0 O xv² = c(x+2v) Ox²v² = c(x + v) X V 2 Oxv² = c(2x + v) O xv² = c(x + v)

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Q: Evaluate: ƒ²₁ ³² ²₁ 0 [(x²-y²)²] x+y du de

A: Follow the procedure given below.

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Q: Q9. If W = f(u)=u³ +sin ¹u+lnu, and u= ax +by, where a, and b are constants, show that aw Əw b oy Əx

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Q: The following equation P(t)= 28sin(360/365 t - 1.4) models the position of the sun at sunset, north…

A: P(t)=28 sin360365t-1.4To Find: The significance of the number 1.4 in terms of the DAY of the year?

Q: IV. A small business determined that the price-demand and cost functions for producing and selling x…

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Q: ๆ ³₁₂₁ (4x²y — z³) dz dy dx -2 J1

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A: This question is related to rate of change, we will solve it using given information.

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Q: Evaluate: 3₂₁ [2³(x + y)³] dz dy dx

A: Given: I=∫-23∫-12∫01z3x+y3dzdydx   As we know the Power Rule: ∫ax+bndx=ax+bn+1an+1+C, where a &amp;…

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Q: Evaluate the indefinite integral given below. [(1 (10-20x4) csc² (2x5 - 5x) dx

A: We have to evaluate the indefinite integral ∫10-20x4 csc22x5-5x dx.

Q: What is the magnitude of a projection p = (7,3) on a = (-4, 2)

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Q: lim (sech 2x) csch x² +0x f(x) = csch x

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