(a) Use the definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit. lim n- co i = 1 (b) The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit in part 13 + 23 + 33 + ... + n3 n(n + 1) = 2

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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.