1. Consider the position function 7 (t) = (4 sin(2t), 2,4 cos(2t)). (a) Sketch the path of this curve. Create a table of values with at least three coordinate triples. (b) Find the tangent line to this curve at the point (0, 2, 4). (c) Find the unit tangent vector to this curve. (d) Find the arc length of this smooth curve from t = 0 to t = 1/2. (e) Find the curvature, k(t), of this path at any time t.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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