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Quiz2 - Math 20A(Shenk Quiz 2 Name e-mail address Work alone and use no books notes or calculators Show your work on 8.”‘ × 11” paper and

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Unformatted text preview: Math 20A (Shenk). Quiz 2. August 27, 2007. Name e-mail address Work alone and use no books, notes, or calculators. Show your work on 8.”‘ × 11” paper and staple it to the quiz when you turn it in. 1. Express e iπ in the form a + ib with real numbers a and b . 2. Use Euler’s formulas to show that sin ( 1 2 π- x ) = cos x for all x . 3. Does the improper integral integraldisplay ∞ 4 1 x 5 / 2 dx converge? If so, find its value. 4. Does the sequence a n = 2 +(- 1) n , for n = 0 , 1 , 2 , . . . converge, diverge to ∞ , diverge to-∞ , or diverge without a limit? 5. Find the value of 2 + 2 2 + 2 3 + 2 4 + ··· + 2 10 . 2 8 = 256 2 9 = 512 2 10 = 1024 2 11 = 2048 6. Does the series ∞ summationdisplay j =0 (- 1 4 ) j converge, diverge to ∞ , diverge to-∞ , or diverge without a limit? If it converges, give its value. 7. You open a new savings account and make $100 deposits at the beginning of each month for five years. You don’t make any other deposits or withdrawals. The account earns 12% annualfive years....
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Quiz2 - Math 20A(Shenk Quiz 2 Name e-mail address Work alone and use no books notes or calculators Show your work on 8.”‘ × 11” paper and

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