For each of the following sequences find the set S of subsequential limit points, the limit superior and limit inferior. Include too as possible limits. (a) (In) = (0, 1,2,0, 1,3,0, 1, 4,...) (b) I, = n(2+ (-1)"). (c) I, = n COS

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Q: v) How would the value of the previous limit change if instead of the function y = words, what is 4…

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Q: 5. For the following sequences find the limit superior, the limit inferior and determine whether…

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Q: Question 4.[4, 4 marks] Evaluate the following limits, 1+ x (a) lim [r – a* In(-")I (b) lim(1- 2r)

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Q: 5) Compute the following limit if it exists 2 (x+y)³² - (x-g) ty lim (x,y)=(0,0) (012)

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Q: b) lim cos(x) – 1

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Q: i. Find the limit of the following. 4n -2n + 4n 2n +7 n+4 n – 5n+6 a) lim n - 2n 5n -3n b) lim -16…

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Q: 4 ху x y* .8 x* + y b. lim (x,y)→(0,0)

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.