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Calculus - Curl and divergence - Double Integral

Question (1)
Write the Taylor series with center zero for the function f(x) = In(1 + x^2 )

Question (2)
Compute the first-order partial derivatives of f(x, y) = 2x/(x-y)

Question (3)
Evaluate the double integral (1 to 3)(0 to 1) of (2x-3y)dx dy

Question (4)
Calculate the divergence and curl of the vector field
F(x, y, z) = 2xi + 3yj - 4zk.

For the full description of the questions in mathematical font and format, please download the attached questions file.

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Solution Preview

Solution (1)
If f(x) is the given function, then the Taylor series about x = a is ........
Differentiating the given function f(x) with respect to x , we get ........
f '(0)= 0 , f ''(0) = 2 , f '''(0) = 0 ...

Solution Summary

Solutions to the problems in the attached file are given with step by step explanation using all the formulas and working in such a manner that the student could easily understand the procedure to solve such type of problems.
Students can use these solutions as model solutions to solve other similar problems.