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Find the limit, if it exists. If the limit does not exist, explain why.

$ \displaystyle \lim_{x \to 0.5^-}\frac{2x - 1}{| 2x^3 - x^2 |} $

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position?

How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?

How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if.(i) 4 letters are used at a time,(ii) all letters are used at a time,(iii) all letters are used but first letter is a vowel?

In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?

In how many ways can the letters of the word PERMUTATIONS be arranged if the(i) words start with $\mathrm{P}$ and end with $\mathrm{S}$,(ii) vowels are all together,(iii) there are always 4 letters between $\mathrm{P}$ and $\mathrm{S}$ ?