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Assume that (X, d) is a metric space and let (x1, : : : , xn) be a nite set of pointsof X. Elustrate , using only the de nition of open, that the set X\(x1, : : : , xn) obtained by removing every xi from X is open in X. (Sketch a picture to get some intuition!)
Short Cuts for solving quadratic equations
Metallic spheres of radii 6 centimetre, 8 centimetre and 10 centimetres respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
program of curve revolve and create a surface
Illustration 1 In a described exam the scores for 10 students were given as: Student Mark (x) |x-x¯| A 60
The price of gasoline is $1.349 cents per gallon. If the price increases through three tenths of a cent, what will the price of gasoline be? Three tenths of a cent can be writt
What inequalities and intervals are? If it is given that a real number 'p' is not less than another real number 'q', we understand that either p should be equal to q or
Q. Definition of Random Variables? Ans. Up to this point, we have been looking at probabilities of different events. Basically, random variables assign numbers to element
Prime number A prime number is a number whose only +ve factors are 1 and itself. For instance 2, 3, 5, and 7 are all of the examples of prime numbers. Examples of numbers whic
Assume E is the event that a randomly generated bit string of length 4 starts with a 1 and F is the event that this bit string consists of an even number of 1's. Are E and F indepe
The interval of validity for an IVP along with initial conditions: y(t 0 ) = y 0 or/and y (k) (t 0 ) = y k There is the largest possible interval on that the solution is va
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