Gradient

Please see the attached PDF file. Thanks.

Maximum

Please see the attached PDF file. Thanks! I would like someone other than OTA#103746 or 101620 to attempt a solution.

Convergence Problem

Please tell me if the following (see attached) series converge. This is a problem from my text book and unfortunately there are no solutions for this problem. I need justification, not just a yes it converges or no it doesn't answer. I tried the root and ratio test, but neiter of these works. Thanks

Spherical Volume

I would prefer a solution in PDF format. Thanks!

Matrix Series

I would prefer a solution in PDF format. Thanks!

Brouwer's Fixed Point Theorem

I would prefer a solution in PDF format. Thanks!

Mean Value Theorem for Harmonic Functions

Please see the attached PDF file. I would prefer a solution in PDF format. Thank You.

Euler Equation of Hydrodynamics (CORRECTED)

I corrected the problem statement which had a typo in the Euler Equation, sorry. Please see the attached PDF file. I would prefer a solution in PDF format. Thanks!

Harmonic Functions

Please see the attached PDF file. I would prefer a solution in PDF file and would like someone other than OTA#103300 to attempt a solution. Thank You.

Volume of a Sphere

Please see the attached PDF file. I would prefer a solution in PDF format and someone other than OTA#103860 to attempt a solution. Thanks.