# 4) Compute 1 dz dr dy and give a geometric interpretation of your answer.

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Q: dz Let z = a? + y, x = 2st, y = s- t, s = u", and t= u sin w. Compute for and du %3D

A: We have that z=x2+y3x=2sty=s-t2s=uwt=usinw We will find ∂z∂w and ∂y∂u

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Q: 3 se (z, y) # (0,0) f(r, y) = 2r2 +y? 1 se (r, y) = (0,0)

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Q: 1. How many terms are there in an arithmetic sequence where a̟ = 12,an = 60 and d = 8? %3D

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Q: Q26: Define the integral domain ring. Is every ring an integral domain?

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Q: Q26: Define the integral domain ring. Is every ring an integral domain?

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Q: 5. E=Z+, (a*b) = (a· b)/5 6. F= Q, (a*b) = (Imax(a,b)]/b) - 9

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Q: find the all solutions of eguation 2-lo2+25 =-1+3i

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Q: 1. Consider A = (0,4, 2), B = (6, 0,0) and C (3,0,-1). (a) Find the unit vector in the same…

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Q: 7. G=Z+, (a*b) = |min(a,b)l/a 8. H= Q+, (a*b) = (a+b) + 10 *wh %3! %3!

A: This is not closed , because Take a=2, b=1 Then a*b= 1/2 and this does to belongs to Z+ Therefore it…

Q: Question Romberg integration for approximating f(x)dx gives R21 then f(1) = = 3 and R,, = 3.12 4.01…

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Q: 2. B=Z, (a*b) = a+b 3. C=Z+, (a*b) = ([max(a,b)]/8) + 3 4. D= Q+, (a*b) = (a · b)/4 5. E=Z+, (a*b) =…

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