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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.


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.