8. Suppose that over a region of space the electrical potential V is given by V(x,y,z) = 5x² – 3xy + xyz, find the following: - a) Compute the rate of change of the potential at P (3, 4,5) in the direction of the vector v = (1,1, –1). b) In which direction does V change the most rapidly at P? c) Find the maximum rate of change at P.
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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