Select the second function in "Limits at Infinity", y (2x2 -x(3x2 -x+ 1) lim f(x) (a) With the default view 0 s xs10, estimate the value of L X co (b) Set e 0.06 and use the N-slider below the graph to find the smallest value for N so that the portion of the curve to the right of x = N is contained in the interval (L E, L+e) (c) Change the graph view to 0sxs 50. Is the curve to the right of x = N still contained in the interval (L - e, L + e)? Yes No Should you revise your estimate for the value of the limit? Yes No (d) Click Zoom in and expand the graph view to 0sx 500. Set the estimated limit value to 0.667 and e = 0.002. What is the smallest value of N that satisfies the limit definition? lim (2x2 - x/(3x2 - x + 1) using the techniques of Section 2.5 X co (e) Compute the value of

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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.