Calculus Tutorial

May 19th, 2015
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Prove that if lim┬(x→a)⁡〖f(x)〗=l, then lim┬(x→a)⁡|f(x)|=|l|. Is the converse is true ? Justify your answer. Let f be defined on D and let f(x)≥0 for all x∈D. If lim┬(x→a)⁡〖f(x)〗 exists, then show that lim┬(x→a)⁡〖f(x)〗≥0.

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PM 1001- Calculus ITutorial 041. Prove that if , then . Is the converse is true? Justify your answer.2. Let be defined on and let for all . If exists, then show that .3. Let and be defined on and let for each . If and exist, then show that .4. Show that does not exists.5. Using the difinition of limit, prove the followings .a) b) c) d) e) on (0,2)f) on (2,4)g) for h) i) j) 6. Give examples to show that if and then may tend to a finite limit, + or or oscillate.7. Let given by . Using the definition of continuity, prove that is continuous on.

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