Calculus Review Solutions

  1. h=\frac{1}{\sqrt{3}} r=\frac{\sqrt{6}}{3}

2. a. Q=\frac{3000}{\sin\theta}+6000-\frac{1500}{\tan\theta} b. \theta=\frac{\pi}{3}

3. \frac{dT}{dD}=\frac{3CD^2}{2}-\frac{4D^3}{3}

4. left and right hand limits don’t agree

5. 0

6. left and right hand limits don’t agree

7. -\infty

8. 54

9. (-\infty,1)\cup (1,\infty)

10. \frac{-2}{x\sqrt{1-(\ln{x^2})^2}}

11. x^{\sin{x}-1}\cos{x}\sin{x}+x^{\sin{x}}\cos^2{x}\ln{x}-x^{\sin{x}}\sin{x}

12. \frac{dy}{dx}=\frac{-\sin{x}-2x}{2y+1}

13. \frac{-33}{2}

14. \frac{-\pi}{3}

15. -1

16. f(x)=\frac{-x^4}{12}+\frac{x^3}{3}-\frac{4x}{3}

17. f'(-1)<\int_{-1}^1g(x)dx<\int_0^{\frac{1}{2}}(g(x)-f(x))dx<\int_{\frac{-1}{2}}^0f(x)dx<g'(0)

18. 18

80 feet

19. \ln{x}+\cos{x}+C

20. 20

derivatives review solutions

limits review answer sheet

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