Modern Computing for Mathematicians (Math 587)
Written Assignment No. 4

1.  Directions

Use GELLMU to write solutions for the following Calculus III exercises.

Re-state each exercise before presenting its solution. Write each solution carefully as if it were to be included as an example in a calculus textbook.

Submit in writing:

• A verbatim listing of your generalized LaTeX source.

• A printout of the PDF output.

• A verbatim listing of the <math> element in the XHTML + MathML output file that has the greatest length as a string.

• The URL in your website at www.albany.edu where your XHTML + MathML output may be found.

Note that this assignment sheet originated with the GELLMU source amcm090407.glm.

2.  Exercises

1. Find the equation of the plane in R^{3} passing through the point (1, -2, 2) that is parallel to the plane given by the equation

   2x - 3y + z  =  0    .

2. When

   g(x, y, z)  =  xz + y e^{x}

   find the second order partial derivatives:

   (a) {partial^{2} g}/{partial x^{2}}         (b) {partial^{2} g}/{partialzpartialx}         (c) {partial^{2} g}/{partial y^{2}}

3. Find the equation of the plane in R^{3} that is tangent at the point (6, -3, 1) to the ellipsoid given by the equation

   {x^{2}}/{4} + {y^{2}}/{9} + z^{2}  =  11    .