M254ReviewTestASoln

M254ReviewTestASoln - x = 0 for the following(a cos x = 1-x...

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Name: TA: Section: Review Test (version A), Math 254 January 24, 2008 1. (10 pts) Calculate the following derivatives: (assume a, b, c , and k are constants): (a) w = 5 - 3 x 5 + 3 x , w 0 = - 30 (3 x + 5) 2 (b) r ( t ) = ln ± sin ± t k ²² , r 0 ( t ) = cot ( t k ) k 2. (20 pts) Calculate the following integrals: (assume a, b, c , and k are constants): (a) Z cos 3 2 θ sin 2 θ dθ = - 1 8 cos 4 2 θ + C (b) Z ( x 2 - 3 x + 2 ) e - 4 x dx = - 1 32 e - 4 x ( 8 x 2 - 20 x + 11 ) + C 3. (10 pts) Give the first four non-vanishing terms of the Taylor series expanded near
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Unformatted text preview: x = 0 for the following: (a) cos( x ) = 1-x 2 2! + x 4 4!-x 6 6! + ··· (b) √ 1 + x = (1 + x ) 1 / 2 = 1 + x 2-x 2 8 + x 3 16 + ··· 4. (a) (5 pts) Write 2 e i 7 π/ 6 in the form a + ib =-√ 3-i (b) (5 pts) Write-1-i in the form re iθ . Angles are in radians. √ 2 e-i 3 π 4...
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