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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.
Estimating the Value of a Series One more application of series is not actually an application of infinite series. It's much more an application of partial sums. Actually, we
Gm signal is better than am signal becuase
? (2x+3)dx
In pharmaceutical product research doctors visit the place to learn what
What is Plotting Points ? How would you go about drawing the graph of y = x2 ? One way to do it is by plotting points. (Your graphing calculator uses this method.) This is
verify liouville''s theorem for y''''''-y''''-y''+y=0
Illustration: Find the solution to the subsequent IVP. ty' + 2y = t 2 - t + 1, y(1) = ½ Solution : Initially divide via the t to find the differential equation in
Given, y = f(x) = 2 x 3 - 3x 2 + 4x +5 a) Use the Power function to find derivative of the function. b) Find the value of the derivative at x = 4.
Terry earns $680 per week. He is entitled to 4 weeks annual leave and receives an additional holiday loading of 17.5%. Calculate his total pay for this holiday period.
I need the coordinates for this equation Y=1/2-4
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