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# 5 - 82 Prob 11 1 3 x 9 x 2 2 9 x 3 2 Prob 12 P 4 x = x-x 2...

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Solution set for Math 155, of Assignment 5 Prob. 1 The integral is improper because the integrand is discontinuous in the interval. Its value is 6 . Prob. 2 The integral is divergent. Prob. 3 The integral is divergent. Prob. 4 (a) For x > 0 , x 2 = x 4 < 1 + x 4 , since the square root function is increasing. (b) We know that 1 1 x 2 dx is convergent, so, by part a), so is 1 1 1 + x 4 dx. Prob. 5 Convergent, compare with 1 1 x 2 dx . Prob. 6 1 . 00645 . Prob. 7 0 . 32609 . The exact value is 0 . 3504 ... Prob. 8 - 0 . 399166 . The exact value is - 0 . 350402 ... Prob. 9
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Unformatted text preview: 82 . Prob. 11 1 + 3 x + 9 x 2 2 + 9 x 3 2 . Prob. 12 P 4 ( x ) = x-x 2 2 + x 3 3-x 4 4 . ln ( 1 + . 2 ) = . 18232155 ... , P 4 ( . 2 ) = . 1822666666 ... . Prob. 13 P 3 ( x ) = x-1-1 2 ( x-1 ) 2 + 1 3 ( x-1 ) 3 . ln 2 = . 693147180559 ... , P 3 ( 2 ) = . 83333333 ... Prob. 14 P 3 ( x ) = -1 + 1 3 ( x-1 ) + 1 9 ( x-1 ) 2 + 5 81 ( x-1 ) 3 . (-. 9 ) 1 / 3 = . 965489 ... , P 3 (-. 9 ) = -1 . 65561 ... 1...
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