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Theorem If {a n } is bounded and monotonic then { a n } is convergent. Be cautious to not misuse this theorem. It does not state that if a sequence is not bounded and/or
1. For a function f : Z → Z, let R be the relation on Z given by xRy iff f(x) = f(y). (a) Prove that R is an equivalence relation on Z. (b) If for every x ? Z, the equivalenc
sin 4 x - sin x = 0
Function notation: Next we have to take a rapid look at function notation. Function notation is nothing more than way of writing the y in a function which will let to simplify not
X and Y are centers of circles of radius 9cm and 2cm and XY = 17cm. Z is the centre of a circle of radius 4 cm, which touches the above circles externally. Given that XZY=90 o , w
A piece of cardboard in the shape of a trapezium ABCD & AB || DE, ∠ BCD = 900, quarter circle BFEC is removed. Given AB = BC = 3.5 cm, DE = 2 cm. Calculate the area of remaining p
Consider the Solow growth model as given in the lecture notes using the Cobb-Douglas production function Y t = AK 1-α t L α t a) Set up the underlying nonlinear differen
give me the anwsers ..
Some important issue of graph Before moving on to the next example, there are some important things to note. Firstly, in almost all problems a graph is pretty much needed.
Graph f ( x ) = |x| Solution There actually isn't much to in this problem outside of reminding ourselves of what absolute value is. Remember again that the absolute value f
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