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1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies.
1. C(n) = 3C(n/2) + n
2. G(n) = G(n - 1) + 1/n
3. I(n) = I(n/2) + n/ lg(n)
2. Define a (p,q)-tree as a rooted tree where every internal node has between p and q (inclusive) children. Use the Master Theorem to give asymptotic bounds for the height of the tree. You can assume both p and q are constants with 2 ≤ p ≤ q.
3. (‡) Dominos
A 2 × 10 rectangle filled with ten dominos, and a 2 × 2 × 10 box filled with ten slabs.
1. A domino is a 2×1 or 1×2 rectangle. How many different ways are there to completely fill a 2 × n rectangle with n dominos?
2. A slab is a three-dimensional box with dimensions 1 × 2 × 2, 2 × 1 × 2, or 2 × 2 × 1. How many different ways are there to fill a 2 × 2 × n box with n slabs? Set up a recurrence relation and give reasonable exponential upper and lower bounds.
Give the Introduction to amino ACID and nucleotide metabolism ? Here, we studied about the chemistry of proteins and amino acids. We studied that the amino acids are used for p
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how to solve this? y = 7x - 12 y = x2 Solve the system using substitution.
Previously discussed how important it is to expose children to a variety of verbal problems involving the concept that they are trying to learn. Children attach meaning to the abst
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Q. Sum and Difference Identities? Ans. These six sum and difference identities express trigonometric functions of (u ± v) as functions of u and v alone.
What is modi method?
Left-handed limit We say provided we can make f(x) as close to L as we desire for all x sufficiently close to a and x Note that the change in notation is extremely m
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