someone comes up with another definition of convergence. He defines an → L by saying that there exists a constant C > 0 such that |an − L| < C/n . Write a couple of sentences analysing his definition and discuss whether or not it is correct either proving or disproving equivalence to the correct definition.

Q: Which of the following statement(s) is/are TRUE ? When the function f is differentiable, Newton's…

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Q: Show that there is only one way to write ƒ asthe sum of an even and an odd function. (Hint: One way…

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Q: 2. Suppose that f is an increasing function on the interval [a, b]. Let F(t) = %3D a.) Argue that if…

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Q: A balanced ternary string of length n is a function f : [n] → {-1,0, 1}. The weight of such a string…

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Q: Consider functions f: {1,2,3, 4} → {a, b, c}. i. How many such functions are there? ii. How many…

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Q: Calculate the set op Convergence X72

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Q: (c) If each fn has a finite number of discontinuities, then f has a finite numberof discontinuities.

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Q: Suppose that a friend tells you that if any number M > 0 were to be speci- fied, one would always be…

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Q: 2. Let f be the arithmetic function defined by f(n) = (-1)". Compute Z;(2) = f(n) n2 n=1 Hint:…

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Q: If f is continuous on the interval [5, 12] and f(5) = 7 and f(12) = -2, then f must have at least…

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Q: If n= any integer, show that the function f(z) +[- z] has %3D removable discontinuity at x-n, here…

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Q: (2) Show that C(0, 1] C L'(0,1]. Compare |flsup and fl. Justify your answer. Generalize this to the…

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Q: f = 0(g) implies g = (f).

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Q: For each of the following two statements, give a counterexample to show that the state- ment is…

A: Counter examples for given statements to show false are:

Q: 29 107 25 E

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Q: What is the value (i.e. what do we learn) from using the Wronskian on a set of functions?

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Q: Suppose the function f has the property that there exists a number B such that |S(x) – f(c)| < B|x –…

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Q: 5. Show that the sum f(x) = g(x) + h(x) is convex if both g and h are. Use this result to show that…

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