Suppose that w = f(x, y, z), where x = x(u, v), y = y(u, v), and z = =z(u, v). Which of the following make sense mathematically and are written with the correct Leibniz notation Jw dx w dz dw dy + dy dv dx dv Oz dv 0 dw ลบ Ow Ox - UNIS ลพ dw dx du ?х ди θω Ow dre du da du dw მა dw dv 11 дw Ju du əx - + dw dx ах дv Submit Question + dw dx da av + + + + Əw əv dv da dw dy dy du dw dy dy du dw dy dy dv dw dy dy du + + + + Əw əz Əz du dw dz Əz du dw dz Əz dv dw az dz əv www

Q: 20. Use u substitution to evaluate. S secrtant 1+secx dx

A: Evaluation of the indefinite integral by substitution method

Q: Use the Einstein notation to prove the following: (a) ax(bxc) = (a c)b-(a b)c (b) VX Vf = 0 (c)…

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Q: X=4uv-2u, y= - (uv +8uvw), and Z:9uvw Find acx.y,z) =

A: We have to find Jacobian.

Q: 2. J Зу /7—Зу?dy

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Q: cos ㅇㅎ 。 3 1층 2 ㅇㅠ 으뜸 3

A:

Q: 1 d) S e) S csc³x cot³x dx f) S dx x2Vx2 + 4 dx

A:

Q: d 1) Find sec dt 2)

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Q: dw 21. : 1-cosw A. -tan w + secw + C B. w – cotw + C C.-cotw – cscw + C_ D. -cscw + tanw + C

A: We can find the integral value as below.

Q: Suppose f(u, v) = ue", where u = rs and v = r+ s. Which of the following is equivalent to –? dr af…

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Q: If find az/au and az/av. дz/?u = Əz/dv= z = xe", x=u³v³, y=u³+v³₂ (In your answers, do not rewrite…

A: z=xeyx=u3-v3y=u3+v3from chain rule ∂z∂u=∂z∂x×∂x∂u+∂z∂y×∂y∂u

Q: Suppose u = (4, 1, 1) and v = (–4, −1, −3). Then: u + v= Ա υ V= u= 2u= -1/v= 7u - 6v=

A: