Nathaniel and Anna are thinking about the function g: (1, o0) → R given by 9(x) = 26/(1-2) Nathaniel wants to calculate lim g(x). Anna says, "Oh no, this limit is an indeterminate form!" What type of indeterminate form is this limit? O 0-0 o (-1)0 o 00 O 00 o 10 o 10 O o0 00 Nathaniel says, "That's okay, I have a plan. Let's write g(x) = en(x) for some new function h." Anna says, "I see! Then we can write h(x) without any exponentiation." Write h(x) in simplified form (that is, without any exponents, and only in terms of x): h(x) = Anna continues, "I'm still not sure about the original limit, but I do know how to find a similar limit of this new function." What is lim h(x)? lim h(x) = Number Nathaniel correctly states, "Since the exponential function is (Click for List) , we can finally evaluate the original limit." What is the original limit? lim g(x) =

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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.