4. Show that f(x) = sin(x² + 3x) is equal to g(x) = -x cos(x) at least once on Hint: Think about the IVT. 6.
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.
ONLY ANSWER QUESTION NUMBER 4! (IGNORE 3)
Intermediate Value Theorem (IVT) :
It states that if a continuous function f(x) on the interval [a,b] has values of opposite sign inside an interval, then there must be some value x=c on the interval (a,b) for which f(c)=0.
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