Math 291 Lab 3 Due Monday February 5, 2018

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 (.tex) file and your compiled document (in either .dvi or .ps or .pdf form).

You will be graded on both your raw TEX code and the accuracy of your compiled document. Don’t forget to name your file in the format of JaneDoeLab2.tex and include a name block similar to the one described in Lab 1.

1. Use the enumerate environment to automatically number things as in Lab 2. [Double-check when you are done that your numbers go up through 4, since there is a second page.]

2. Typeset each of the following (pay close attention to which display mode is being used: in-line, displayed, or hybrid, and whether or not there are equation numbers):

(a) lim_{x→2^{+}} (\frac{1}{x−2}) = +∞

(b) A = ∑_{i=1}^{n} \frac{2}{3} (f (x_{i}))^{3} Δx_{i}

(c)

A = ∫_{θ_{1}}^{θ_{2}} \frac{1}{2} [r_{o}^{2} − r_{i}^{2}] dθ

[Note: To get the right amount of space between the integrand and the differential (the dθ), use a “\,”.]

(d)

f^{+}(x) = lim inf_{h→0^{+}} \frac{f(x + h) − f(x)}{h}  (1)

(e)

[(|\frac{⋃_{λ∈Λ} A_{λ}}{⋂_{λ∈Λ} \overline{B}_{λ}} |)]\}_{0}^{10}

3. Typeset each of the following expressions. You will need to hunt down some special symbols for some of these.

(a) d̄+ r̃ + â + ǵ = ȯ − n̈

(b) 12i⃗ + 8j⃗ − 3k⃗ − (3i⃗ − 5j⃗ − 4k⃗) = 9i⃗ + 13j⃗ + k⃗

(c) x̃yz + p̂dq

(d)

\overline{\overline{y}^{2} − \overline{z^{2}}} + \overleftarrow{\underline{y_{2}} − \underline{z}_{2}}
(e) \binom{n}{k} =^{def} \frac{n!}{k! (n − k)!}

(f)

\underbrace{x · x · . . . · x}_{10 times} = x^{10}  (2)

4. Typeset the following equations:

A_{1} = T_{1} ∩ ⋯ ∩ T_{n}  (3)
A_{2} = T′_{1} ∩ ⋯ ∩ T′_{n}  (4)
A_{1} ∩ A_{2} = (T_{1} ∩ ⋯ ∩ T_{n}) ∩ (T′_{1} ∩ ⋯ ∩ T′_{n})  (5)