# 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

18.

80 feet

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

20.

derivatives review solutions