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show that the circle described on any focal chord of the parabola touches the directrix
Determine if the following sequences are monotonic and/or bounded. (a) {-n 2 } ∞ n=0 (b) {( -1) n+1 } ∞ n=1 (c) {2/n 2 } ∞ n=5 Solution {-n 2 } ∞ n=0
Both need to be a full page, detailed proof. Not just a few lines of proof. (1) “Every convergent sequence contains either an increasing, or a decreasing subsequence (or possibly
Area of the equilateral triangle: Given : D, E, F are the mind points of BC, CA, AB. R.T.P. : We have to determine the ratio of the area of of triangle DEF and triangle AB
Problems Involving Motion - Word Problems: How far can a car travelling at a rate of 52 miles per hour travel in 2½ hours? Solution: Using Equation 13: s = vavt
If a differential equation does have a solution how many solutions are there? As we will see ultimately, this is possible for a differential equation to contain more than one s
1. How many closed necklaces of length 7 can be made with 3 colors? (notice that 7 is a prime) 2. How many closed necklaces of length 10 can be made with 3 colors (this is di erent
A vertical post stands on a horizontal plane. The angle of elevation of the top is 60 o and that of a point x metre be the height of the post, then prove that x = 2 h/3 .
What is minimum spanning tree? Determine a railway network of minimal cost for the cities in the following graph using Kruskal's algorithm. Ans: Minimum spanning tree in a con
Determine the general solution to 2t 2 y'' + ty' - 3y = 0 It given that y (t) = t -1 is a solution. Solution Reduction of order needs that a solution already be iden
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