d d Calculate ri(t) r2(t)] and ri(t) x r2(t)] first by differentiating dt' dt the product directly and then by applying the formulas d dr2 dri (t) r2(t)] = r1(t) - r2(t) and dt dt dt dr2 dri d [r(t) x r2(t)] = r:(t) x x r2(t). dt dt dt ri(t) = 3ti + 2t°j + 4t°k, r2(t) = t*k d [ri(t) r2(t)] dt d [r1(t) x r2(t)] dt

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A: I have provided this answer with full description in step-2.

Q: ft号+号 13 4. 4 2.

A: We can solve this as follows:

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Q: d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating d dt dt the product directly…

A: We know, d/dt (r1(t).r2(t))= r1(t).dr2(t)/dt + r2(t).dr1(t)/dt

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A: Here, the given series is: ∑n=2∞(n-3)Anxn-5...(1)

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Q: In x2/25+ x² dx , we let x = 5sine. (A) True False

A: FALSEHere , the correct substitution is x=5tanθ differentiatate On both sidesdx= 5 sec2θ…

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A:

Q: 2 Integrating factors found by inspection.: fr -y +1}tr=x{x² - y² -1y=0

A: Given

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A: The given differential equation is  2y(x+y+2)dx+(y2-x2-4x-1) dy=0. Repost the next question.

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Q: Complete

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Q: 1. Linear equation of order one: dy-x -2xy zx = 0

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Q: Given f″(x)=−36sin(6x)f″(x)=−36sin⁡(6x) and f′(0)=−6f′(0)=−6 and f(0)=2f(0)=2. Find f(π/5)

A: f''(x)=-36 sin(6x)f'(x)=∫-36 sin(6x) dxf'(x)=-36 -cos(6x)6+Cf'(x)=6cos(6x)+Cf'(0)=-6-6=6 cos(0)…

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Q: 1. Linear equation of order one: dy-(r-2ydx =0

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Q: Linear equation of order one: dy- (x² – 2xy ldx = 0

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A: