course mth 272 ??????K?+????}?assignment #021
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20:44:17 Query problem 6.6.14 integral from -infinity to infinity of x^2 e^(-x^3)
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RESPONSE --> first you apply the definition of the improper integral integral from -infinity to infinity of x^2 e^(-x^3) = integral from -infinity to c of x^2 e^(-x^3) + integral from c to infinity of x^2 e^(-x^3) antiderivative = x^3 / 3 * (e^-x^3) (-3x) x^3 / 3 * (-1/3e^-x^3) apply fundamental theorem with -infinity to c and c to infinity answer = the integral will diverge bc -infinity to c will diverge and it only takes one of the integrals on the right to make the integral on the left diverge. confidence assessment: 2
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20:44:48 Does the integral converge, and if so what is its value? Explain why the integral does or does not converge.
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RESPONSE --> No the integral does not converge. This was explained in previous answer. confidence assessment:
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21:07:11 Query problem 6.6.40 (was 6.6.38) farm profit of $75K per year, 8% continuously compounded, find present value of the farm for 20 years, and forever.
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RESPONSE --> = integral from 0 to 20 of 75,000e^-.08t dt = [(75,000 / -.08)e^-0.08t] at 0 and 20 or at 0 and infinity apply fundamental theorem for 20 years for 20 =371477.4318 for 0 = 75000 =$296,477 for forever apply fundamental theorem for infinity = b = 0 for 0 =75000 0 - 75000 = -$75000 confidence assessment: 2
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21:07:29 What is the present value of the farm for 20 years, and what is its present value forever?
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RESPONSE --> already answered confidence assessment:
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21:08:07 What integrals did you evaluate to get your results?
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RESPONSE --> already answered 0 to 20 and 0 to infinity which is 0 to b confidence assessment: 2
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