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Mathematics LibreTexts

Section 1.2 Answers

  • Page ID
    26455
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    1. \(3\)

    2. \(2\)

    3. \(1\)

    4. \(2\)

    13. \(y=-\frac{x^{2}}{2}+c\)

    14. \(y=x\cos x-\sin x+c\)

    15. \(y=\frac{x^{2}}{2}\ln x-\frac{x^{2}}{4}+c\)

    16. \(y=-x\cos x+2\sin x+c_{1}+c_{2}x\)

    17. \(y=(2x-4)e^{x}+c_{1}+c_{2}x\)

    18. \(y=\frac{x^{3}}{3}-\sin x+e^{x}+c_{1}+c_{2}x\)

    19. \(y=\sin x+c_{1}+c_{2}x+c_{3}x^{2}\)

    20. \(y=-\frac{x^{5}}{60}+e^{x}+c_{1}+c_{2}x+c_{3}x^{2}\)

    21. \(y=\frac{7}{64}e^{4x}+c_{1}+c_{2}x+c_{3}x^{2}\)

    22. \(y=-(x-1)e^{x}\)

    23. \(y=1-\frac{1}{2}\cos x^{2}\)

    24. \(y=3-\ln (\sqrt{2}\cos x)\)

    25. \(y=-\frac{47}{15}-\frac{37}{5}(x-2)+\frac{x^{5}}{30}\)

    26. \(y=\frac{1}{4}xe^{2x}-\frac{1}{4}e^{2x}+\frac{29}{4}\)

    27. \(y=x\sin x+2\cos x-3x-1\)

    28. \(y=(x^{2}-6x+12)e^{x}+\frac{x^{2}}{2}-8x-11\)

    29. \(y=\frac{x^{3}}{3}+\frac{\cos 2x}{6}+\frac{7}{4}x^{2}-6x+\frac{7}{8}\)

    30. \(y=\frac{x^{4}}{12}+\frac{x^{3}}{6}+\frac{1}{2}(x-2)^{2}-\frac{26}{3}(x-2)-\frac{5}{3}\)

    40. 

    1. \(576\) ft
    2. \(10\) s

    41. 

    b. \(y=0\)

    43.

    a. \((-2c-2,\infty )\: (-\infty ,\infty )\)