Math 291 Lab 1

Instructions: Use L^{A}TEX to typeset a document containing each component described below. Turn in your lab by emailing it to fagerstrom@mnstate.edu. You should email both your raw .tex file and your compiled document (in .dvi, .ps, or .pdf form, as long as it can compile to that form). You will be graded on both your raw L^{A}TEX code and the accuracy of your compiled document.

1. Make a name block for your lab containing your name, the name and course number for this class, the date (either when submitted or when due), and “L^{A}TEX Lab 1”. Your name block should be flush right on the page. [A similar name block should appear on all future labs.]

2. Typeset the following mathematical formulas exactly as they are given below, each on a new line.

(a) 7x^{15} + 4x^{10} − 9x^{3} + 73x − \frac{1}{3}

(b) 4x^{3} − 7x + \frac{−3}{4} = x^{2}(x^{3} − 7x^{2} + 5)

(c) f(x, y, z) = x^{3}y^{3}z^{3} − 7x^{2}yz^{4} − 12xy^{5}z^{2}

(d) f(x_{1}, x_{2}) = 8x_{2}^{4}x_{1}

(e) \frac{3}{14} + \frac{2}{3} = \frac{37}{42}

(f) \frac{x^{2}−4x−77}{x+11}

(g) \frac{d}{dx}e^{3x} = 3e^{3x}

(h) \frac{d}{dx}x^{n} = nx^{n−1}

(i) e^{−x^{2}}

(j) \frac{\frac{1}{x−1} + \frac{1}{x+1}}{\frac{1}{x} − \frac{1}{x+1}}

(k) \frac{1}{2^{x}} − 2^{\frac{1}{x}} + \frac{1}{2^{\frac{1}{x}}} − 2^{2^{x}} + 2^{2^{2^{x}}}

(l) lim_{x→1} f(x) = f(1) [Note: The command for limit is \lim.]

(m) cos(3x − 1) [Note: Use a guess to get the cosine function that is consistent with the hint for the limit symbol above.]

(n) Typeset the previous expression again, except surround it with $$ on each side instead of just one $ on each side.

(o) Typeset the limit expression again, except surround it with $$ on each side instead of just $.

(p) V = \frac{4}{3}πr^{3} [Note: The command for π is \pi.]

(q) V = \frac{4πr^{3}}{3}