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1) Show that if (a_n)^infinity evaluated at n=1, and (b_n)^infinity evaluated at n=1 are equivalent sequences of rationals, then (a_n) ^infinity evaluated at n=1 is a cauchy sequence if and only if (b_n)^infinity evaluated at n=1 is a cauchy sequence.
2) Let epsilon >0. Show that if (a_n)^infinity evaluated at n=1 and (b_n)^infinity evaluated at n=1 are eventually epsilon-close, then (a_n)^infinity evaluated at n=1 is bounded if and only if (b_n)^infinity evaluated at n=1 is bounded.
Let A be a symmetric and positive definite (SPD) matrix. Is A^-1 ( inverse of matrix A) a SPD matrix? If so, prove it. If not, explain and give an example.
There are 3 boxes. Each box contains several envelopes. Some envelopes have "you lose" written on them. The rest say "you win..." . However, of the ones that say "you win..." , some contain only a piece of paper saying "... nothing" . Each of the ..
Determine the following values
Find the x-coordinate of the points of inflection of f(x) = 47 + 13x + 18x^ 2 + 4x^ 3 - x^ 4
Consider the following linear mapping from C[-pi,pi] into itself: L(f)=integral from -pi to pi of G(x),h(y),f(y)dy for any function f(x) in C[-pi,pi].
Compute the derivative of the function using the difference quotient and find the equation of the line that is tangent to its curve for x=c
For the metric space { N }, the set of all natural numbers, characterize whether or not it has the following properties: compact, totally bounded, has the Heine-Borel property, complete.
Probability that a player's pick wins the grand prize. In a certain lottery, k balls are chosen at random and without replacement from a bin containing N balls numbered 1 through N
What are the most signification concepts that you have learned about the physical and social domains on the basis of your reading and experience with children?
Why is it important to understand linear equations in business? In particular can you provide examples where the relationship between items that can be affected by management and 'items' that management wished to achieve or attain may be 'linear'?
You're at a school fair where one of the games is "Spin the Wheel". Players spin a giant wheel with numbers 1-40. Look at each of the criteria and express the answers as a decimal, fraction and a percentage.
Determine the height of the tree from the given information - Amman measures the angle between his base line and the line of sight to the base of the tree to be 510. How tall is tree, correct to the nearest M?
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