Sheet1 - Math 21B Kouba Challenge Sheet 1 1 Evaluate the...

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Unformatted text preview: Math 21B Kouba Challenge Sheet 1 1.) Evaluate the following sums. 1000 750 83 1 1 . 2 - 3 _ '3 __ a.) 120%) b.) gm“) 2} c.) 222(“4 H3) 98 i+1 200 10,125 d.) 2104i”) e.) Zln(1+1/z’) f.) .2 (3+sini7r) 1:8 1:1 2:734 2)Eltthfll ' 1' 't'l' i 1 . va ua e e O ow1ng 1m1 . ”3’20 i2 +1, i=1 3.) The speed of a runner at time t seconds is given by v(_t) = t2 — t + 2 ft./sec. a.) Sketch the speed graph for 0 g t g 5. b.) What is the runner’s speed when i.) t=0 seconds ? ii.) t:1 second ? iii.) t:5 seconds ? c.) Estimate the distance the runner travels for 0 g t S 5 by using five equal subdi— visions of time on the interval [0, 5] and speeds determined by i.) left endpoints of the subdivisions. ii.) right endpoints of the subdivisions. iii.) midpoints of the subdivisions. TL (1.) Evaluate the following limit : lim v(5i/n) - (5/71) . Explain why the answer n—>oo . 1:1 represents the exact distance covered by the runner for 0 g t g 5. ...
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