Chapter 7 Problems

Thirty chapter problems: 13 from the original book and 17 added for more practice.

Read the chapter problems → · Chapter solutions →

1. Original problem

   For questions 1-3, determine the value of the expansion

   

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2. Original problem

   For questions 1-3, determine the value of the expansion

   

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3. Original problem

   For questions 1-3, determine the value of the expansion

   

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4. Original problem

   For questions 4 and 5, evaluate the infinite sum

   

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5. Original problem

   For questions 4 and 5, evaluate the infinite sum

   

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6. Original problem

   The average liger weighs 6.2lbs at birth. One standard deviation is approximately 1.2lbs.

   What is the probability of a liger weighing between 5 and 6.2 lbs?

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7. Original problem

   The average liger weighs 6.2lbs at birth. One standard deviation is approximately 1.2lbs.

   What is the probability of a liger weighing between 6.8 and 7.4 lbs?

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8. Original problem

   The average liger weighs 6.2lbs at birth. One standard deviation is approximately 1.2lbs.

   What is the probability of a liger weighing between 3.8 and 8.6 lbs?

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9. Original problem

   For the next five questions, evaluate the definite integrals using a five-term Taylor Expansion

   

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10. Original problem

    For the next five questions, evaluate the definite integrals using a five-term Taylor Expansion

    

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11. Original problem

    For the next five questions, evaluate the definite integrals using a five-term Taylor Expansion

    

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12. Original problem · clarified

    For the next five questions, evaluate the definite integrals using a five-term Taylor Expansion

    ${\int }_0^{1/2}\mathrm{xln}(1+x)\mathrm{dx}$

    Corrected calculation: integrating the fifth term x⁶/5 gives x⁷/35. The five-term value rounds to 0.0355.

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13. Original problem

    For the next five questions, evaluate the definite integrals using a five-term Taylor Expansion

    

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14. Added problem

    Evaluate ${\sum }_{n=0}^{\infty }1/n!$.

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15. Added problem

    Evaluate ${\sum }_{n=0}^{\infty }(-1{)}^n/(2n)!$.

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16. Added problem

    Evaluate ${\sum }_{n=1}^{\infty }(-1{)}^{n+1}/(n{2}^n)$.

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17. Added problem

    Evaluate ${\sum }_{n=1}^{\infty }n/n!$.

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18. Added problem

    Evaluate ${\sum }_{n=0}^{\infty }1/(n+1)!$.

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19. Added problem

    Evaluate ${\sum }_{n=0}^{\infty }(-1{)}^n{\pi }^{2n+1}/(6^{2n+1}(2n+1)!)$.

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20. Added problem

    Use four Maclaurin terms to approximate ${\int }_0^{1/2}{e}^x\mathrm{dx}$, and give an error bound.

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21. Added problem

    Use five Maclaurin terms to approximate ${\int }_0^1{e}^{-x^2}\mathrm{dx}$, and bound the error.

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22. Added problem

    Use three nonzero Maclaurin terms to approximate ${\int }_0^{1/2}\left(\sin x\right)/x\mathrm{dx}$, interpreting the value at zero by continuity.

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23. Added problem

    Use four nonzero Maclaurin terms to approximate ${\int }_0^{1/2}\ln (1+x)\mathrm{dx}$, and bound the error.

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24. Added problem

    Approximate ${\int }_0^1\cos x\mathrm{dx}$ with three nonzero Maclaurin terms and bound the error.

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25. Added problem

    Approximate $\ln \left(1.2\right)$ with three nonzero Maclaurin terms and bound the error.

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26. Added problem

    A weight W is normally distributed with mean 10 kg and standard deviation 2 kg. Find $P(8\le W\le 12)$.

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27. Added problem

    A weight W is normally distributed with mean 10 kg and standard deviation 2 kg. Find $P(W\ge 12)$.

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28. Added problem

    A normally distributed random variable has mean μ. What is $P(X\le \mu )$? Explain.

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29. Added problem

    Let X be normally distributed with mean 100 and standard deviation 15. Use a standardized integral or series to find $P(100\le X\le 115)$.

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30. Added problem

    Do a mean and a standard deviation alone determine an interval probability? Explain with an example.

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