5.8. Let R = C[t]. Show that S = R[x]/((x)^(x, t)²) is not flat over R.

Q: 2. Let f:Z→Z be the function given by fAn) =3n+1. a. Is fone-to-one? Briefly explain why. b. Is…

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Q: f(x,y) be defined implicitly as a function of x and y by the 3xyz =exyz Əz Əz yay ax Əz Əz Find and…

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Q: Is there a twice differentiable function f R2R whose best adratic approximation at the point (1,0)…

A: Given problem is from differential calculus in several variables. We have shown that there exists a…

Q: 3. [32] −1 4-3 4. 5. [. |_3 -4 2 1 2 -1 4,

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Q: Let f (x, y) = e3x-49). Find the equation for the tangent plane to the graph of f at the point…

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Q: Which of the following is the parent function for a) f(x) = x b) flx) = x c) fx) = Ix| d) flx) = Vx

A: Given function is y=23x2. We have to find the parent function of y=23x2. The parent function is…

Q: Given the vector-valued functions е ú(t) = e5ti + e−4tj + tk - 3ti - 2t²j+ 3k v(t) find d = dt d…

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: For the function Hlo>x'tle, fnd a)flxth) 5bf(xth)- flx) c) f(x th)-f(x)

A: Given: f(x)=x2+6 To find: a) f(x+h) b)f(x+h)-f(x) c)f(x+h)-f(x)h

Q: Compute the length of the curve r(t) = (4t² + 8, 61²-5, 1³) over the interval 0 ≤ ≤ 2. (Use decimal…

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Q: Let f(x, y) = √√1 + 18xy and let C be the curve given by y = 2x³ for 0 ≤ x ≤ 3. Compute fef ds. (Use…

A: is the curve given by for .We have to evaluate the integration

Q: Compute the length of the curve r(t) = (21, In(t), r?) over the interval 1 <t < 9. (Use symbolic…

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Q: 5. Calculate the divergence of F = (7x², 9y, -52).

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Q: 10. Let F(x, y, z)= y-yz+1 £z+r-z z+xy-y Find a function g such that F = √g.

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Q: (47) Let C be the curve y = 5x where 1 ≤x≤9. Calculate the length of C.

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Q: find the line ariz ation of the followwing function. fcx, y>=J 9z*+I6y² point (1,1). Use what this…

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