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Math 251- Calc I Homework #1 Dr. Tovar Book: Essential Calculus by Stewart Trigonometry 1) If a symmetric hexagon has sides of length a, what is the area of the hexagon. (Show your work.) 2) Explain how a construction worker can insure that a corner is “square” by using a Pythagorean Triplet. 3) In Dr. Tovar's Trigonometry Tutorial there is a list of Pythagorean Triplets, the last of which is 2 13 + 842 = 852. Determine the next Pythagorean Triplet which starts with 142 + ... (Hint: if you can't figure it out, the answer is in the tutorial, read it!) 4) In trigonometry, we base our triangles off of the unit circle. This leads to something absolutely weird and unusual. What is it? 5) In your own words, define each of the following: (You may get help from ANY source!) Types of Functions: single-valued function multi-valued function continuous function domain of a function range of a function 1-1 function monotonic increasing function monotonic decreasing function vertical line test horizontal line test piecewise defined function positive definite function positive semi-definite function negative definite function negative semi-definite function symmetric function odd function even function inverse function periodic function Math 251- Calc I Homework #2 Dr. Tovar Book: Essential Calculus by Stewart 1) In your own words, define each of the following: (You may get help from ANY source!) Properties of Functions: asymptote critical values extremum slope tangent line normal line concave up concave down inflection point independent variable dependent variable single-variable multi-variable arc length local minimum local maximum absolute minimum absolute maximum x-intercept y-intercept fixed points bounded unbounded Specific Functions: elementary functions rational functions pulse functions Heaviside step function signum function Equations: explicit equation implicit equation parametric equations Number Systems: countable infinity uncountable infinity natural numbers whole numbers integers real numbers complex numbers extended real number system Graphs: abscissa ordinate quadrant 2) Fill in the table below: As before, you may use any source. However, keep in mind that the goal is to actually learn the symbols. (Hint: Many of the answers are at http://en.wikipedia.org/wiki/Table_of_mathematical_symbols ) Symbols: Symbol Meaning there exists For all Ʃ Summation Π Product Proportional to Therefore Because ± Plus or Minus Minus or Plus Implies If and only if Defines Approximately Infinity () Open interval [] Closed interval (] Left open interval [) Right open interval Perpendicular Set of Integers Set of Rational Numbers Set of Real Numbers Set of Complex Numbers