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m16c_test3_sample1

# m16c_test3_sample1 - MATH 16C(001 Midterm 3 June 4 1999...

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Unformatted text preview: MATH 16C(001) Midterm 3 June 4. 1999 OOlCJ‘ 1. ( 8 pts) A ball is thrown upward from the ground to a height of 30 ft and each rebound bounces times as high. Find the total distance traveled by the ball ( simplify your answer ). 2. (8 pts.) Find the ﬁrst 4 nonzero terms of the Maclaurin series for f(x) = \/l + 1:2 3. (8 pts.) The ﬁgure below is formed by subdividing a square whose sides have length 1 into four squares of equal size, shading the bottom left square, and then subdividing the upper right square in the same way. If the process continues inﬁnitely, ﬁnd the total of the shaded area. 4. ( 6 pts) Approximate sin(0.4L) using the ﬁrst 3 nonzero terms of Maclaurin series. 5. (8 pts.) Determine if the following series converge or diverge, justify your answer. 6. (11 pts. ) Find the interval and radius of convergence for the power series ”2114—1 :(1 (ll—2+9) ))(16)" °° 1 7. (10 pts) Considr the series 2 ﬂ n41." " a) F ind the partial sums 51. 52. .53, .5'4 and .5”. b) Find lim .57, "4'00 c) Does the series converge or diverge? ................. 1 1 1 d) If the series converges ﬁnd its sum. ( Hint: — = — — n(n — 1) n — 1 n 8. (23 pts) Determine if each of the follow mg series converge or diverge, justify \0u1 answer ‘ n — .3 a (4ptS) ZEN—é“ b. (6 pts) 2W n=l 3° 4n + 1 °° 4 371+2 c. (7 pts) 2 m d. (6 pts) 2 (E — T" ) n=l 'n=1 .2 r 2 9. (8 pts) Use the ﬁrst 4 nonzero terms of a Maclaurin series to approximate f 1'26“ d2? 0 10. (10 pts) Use the Taylors theorem to ﬁnd the ﬁrst 4 terms of the power series for f (1) = 2 + 1 1* centered at c = 1, and then write the power series using sigma notation. EXTRA CREDIT (10 pts) DC a. (4pts) Determine the convergence or divergence of the series 2(2 — 6 11:1 7k)k b. (6pts) Assume that Z (1,, is a convergent series , and Z 1),, is a divergent series. Let Z (3,, be a series 11:1 71:1 n=l 00 with partial sums 5k. Indicate the convergence or divergence of Z c" by putting C for convergence. 1) for divergence and N for no oonclution can be made in the blank space provideded for each part. i)0<c,,<b,,, .............. ii)0<cn<an .............. iii) 0 < an < 0.1 .............. iv) 0 < b" < en .............. v) lim Sn 2 5 .............. vi) lim 5n : oo .............. 71*«36 "a“; ...
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