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Pre-Calc Homework Solutions 335

# Pre-Calc Homework Solutions 335 - Section 8.3 Section 8.3...

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Section 8.3 Exercises 1. (a) The integral is improper because of an infinite limit of integration. (b) E 0 } x 2 d 1 x 1 } 5 lim b E b 0 } x 2 d 1 x 1 } 5 lim b 3 tan 2 1 x 4 5 lim b (tan 2 1 b 2 0) 5 } p 2 } The integral converges. (c) } p 2 } 2. (a) The integral is improper because the integrand has an infinite discontinuity at x 5 0. (b) E 1 0 } ˇ dx x w } 5 lim b 0 1 E 1 b } ˇ dx x w } 5 lim b 0 1 3 2 ˇ x w 4 5 lim b 0 1 (2 2 2 ˇ b w ) 5 2 The integral converges. (c) 2 3. (a) The integral involves improper integrals because the integrand has an infinite discontinuity at x 5 0. (b) E 1 2 8 } x d 1 x /3 } 5 E 0 2 8 } x d 1 x /3 } 1 E 1 0 } x d 1 x /3 } E 0 2 8 } x d 1 x /3 } 5 lim b 0 2 E b 2 8 } x d 1 x /3 } 5 lim b 0 2 3 } 3 2 } x 2/3 4 5 lim b 0 2 1 } 3 2 } b 2/3 2 6 2 5 2 6 E 1 0 } x d 1 x /3 } 5 lim b 0 1 E 1 b } x d 1 x /3 } 5 lim b 0 1 3 } 3 2 } x 2/3 4 5 lim b 0 1 1 } 3 2 } 2 } 3 2 } b 2/3 2 5 } 3 2 } E 1 2 8 } x d 1 x /3 } 5 2 6 1 } 3 2 } 5 2 } 9 2 } The integral converges.
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