# 6th - lim n →∞ n X i =1 2 n ± 5 2 i n ² 10 5 a Use...

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MATH-119 WEEK 6 RECITATION QUESTIONS 1. Given that the graph of f passes through the point (1 , 6) and that the slope of its tangent line at ( x, f ( x )) is 2 x + 1,find f (2) 2. The graph of the velocity function of a car is shown in the figure.Sketch the graph of the position function. 3. The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown.Estimate the distance traveled during this period. 4. Determine a region whose area is equal to the given limit. Do not evaluate the limit.
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Unformatted text preview: lim n →∞ n X i =1 2 n ± 5 + 2 i n ² 10 5. a ) Use Deﬁnition 2(page 320 in Stewart) to ﬁnd an expression for the area under the curve y = x 3 from 0 to 1 as a limit. b ) The following formula for the sum of the cubes of the ﬁrst n integers is proved in Appendix E(A34 in Stewart).Use it to evaluate the limit in part (a). 1 3 + 2 3 + 3 3 + ,...,n 3 = ³ n ( n + 1) 2 ´ 2 1...
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