Example (ii) Let he components ofa Contravariant vector in Gxe) colordinate a system are (2, x') . Fuid ils in (ee) co-ordinate system, under the Co-orduinates change of co-ordinates 7 = (X) #0 and ñ²=x'x. componant 2

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Q: Suppose that f: R² R² is a function such that f (1,2)= the linear approximation. (Use syntax like…

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Q: дz az Use the chain rule to find and Əs Ət əz Əs əz at = = ¹(=), z = tan u = 3s + 5t, v = 5s - 3t

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Q: Verify the orthogonality condition of each of the equations y" - 2xy' - 2ny = 0 11 ( where n is a…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

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Q: Q and Z are vector valued functions Q(-1) = , Q'(-1) = , Q''(-1) = Z(-1) = , Z'(-1) = , Z''(-1) =…

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Q: 3) Consider stress of a body at a particular point is give in the form of Q(x1, x2, X3) = xỉ – x –…

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Q: Find the values of a, b and c that make F=-5y°z7 (ax + bx6ji - 45,8,7(4x10, 107j+ cy°z64x10, 10x7jk…

A: Given that                          F=-5y9z7ax9+bx6i-45y8z74x10+10x7j+cy9z64x10+10x7k we know that…

Q: find    (a)    div(f)   (b)    curl(f) if f=x^2(vector i)+y^2(vector j+2yz(vector k)

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A: Given that a vector A satisfies the vector transformation A'=SA Query is to show that the derivative…

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Q: x^2y''-2xy'+2y=0; y1=x, y2=x^2 Verify that y1 and y2 are linearly independent

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Q: 18 > (a) Find the direction for which the directional derivative of the function f (x, y) = 7xy² +…

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Q: Find a and b such that v-au bw, nhere u-(1, 2) and w- (1. -1) v - (4, 5)

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Q: The equations xy2 + 6xzcos(u) + ye" = 12 and x³yz + xe" - 8u²v² = 24 are solved for u and v as…

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