Definition: The AREA A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles A = lim R, = lim [f(x1 )Ax + f(x2)Ax+...+f(x, )Ax] n00 n00 (a) Use the above definition to determine which of the following expressions represents the area under the graph of f(x) = x from x = 0 to x = 2. 64 A. lim B. lim 64 C. lim n 00 in 64 D. lim i=1 (b) Evaluate the limit that is the correct answer to part (a). You may find the following formula helpful: n² (n + 1)²(2n² + 2n – 1) 15 + 25 + 35+... +n° 12 i=1 Value of limit = WI=WI -WNI:WI

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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.