# Calculus final exam topic breakdown

2 related rates
2 optimization
1 differentiability
5 limits
1 continuity
2 applications
1 antiderivative
5 derivatives
1 max & min

# 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

# Trigonometry Classwork Solutions

1. $x\in\left\lbrace\frac{7\pi}{18},\frac{11\pi}{18},\frac{19\pi}{18},\frac{23\pi}{18},\frac{31\pi}{18},\frac{35\pi}{18}\right\rbrace$
2. $x\in\left\lbrace\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}\right\rbrace$
3. $x\in\left\lbrace\frac{\pi}{12},\frac{5\pi}{12},\frac{7\pi}{12},\frac{11\pi}{12},\frac{13\pi}{12},\frac{17\pi}{12},\frac{19\pi}{12},\frac{23\pi}{12}\right\rbrace$
4. $x\in\left\lbrace\frac{5\pi}{18},\frac{11\pi}{18},\frac{17\pi}{18},\frac{23\pi}{18},\frac{29\pi}{18},\frac{35\pi}{18}\right\rbrace$
5. $x\in\left\lbrace\frac{\pi}{9},\frac{5\pi}{9},\frac{7\pi}{9},\frac{11\pi}{9},\frac{13\pi}{9},\frac{17\pi}{9}\right\rbrace$
6. $x\in\left\lbrace\frac{\pi}{6},\frac{3\pi}{4},\frac{5\pi}{6},\frac{7\pi}{4}\right\rbrace$
7. $x\in\left\lbrace\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\right\rbrace$
8. $x\in\left\lbrace\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}\right\rbrace$
9. $x\in\left\lbrace 0,\frac{\pi}{6},\frac{2\pi}{3},\frac{5\pi}{6},\frac{4\pi}{3},\frac{3\pi}{2}\right\rbrace$
10. $x\approx 1.159$, $x\approx 5.124$

# Trigonometry Classwork 5-23-17

In 1-9, solve each equation for $x$ such that $0\leq x<2\pi$.

1. $2\sin(3x)+1=0$
2. $2\cos(2x)+1=0$
3. $\sec(4x)-2=0$
4. $\sqrt{3}\tan(3x)+1=0$
5. $2\cos(3x)=1$
6. $2\sin{x}\tan{x}-\tan{x}=1-2\sin{x}$
7. $\sec{x}\tan{x}-\cos{x}\cot{x}=\sin{x}$
8. $\tan{x}-3\cot{x}=0$
9. $\tan(3x)+1=\sec(3x)$
10. Solve for $x$ such that $0\leq x<2\pi$ and round to the nearest thousandth: $\cos{x}=0.4$

# Calculus Homework #12 Due 5-25

Calculate the following definite integrals

1. $\int_0^3 (x^2+4x+3)dx$

2. $\int_0^{\frac{\pi}{4}}\sin xdx$

3. $\int_2^5 (x^3-\pi x^2)dx$

4. $\int_1^2\frac{1+y^2}{y}dy$

# Trigonometry Homework #12 due 5-25

Solve each equation for $x$

1. $2\sin{x}=\sin^2{x}+\cos^2{x}$

2. $3\tan^2{x}=1$

3. $\tan{x}-\cot{x}=\frac{\sin{x}-\cos{x}}{\sin{x}}$

4. $\cos^2\frac{x}{5}=\frac{1}{2}$

5. $\csc\left(x+\frac{2\pi}{5}\right)=1$

6. $\sqrt{\frac{1-\cos\frac{x}{4}}{2}}=\frac{\sqrt{3}}{2}$

7. $\tan{x}\cos{x}=0$

8. $\tan{x}=\frac{\sin\frac{5\pi}{6}}{1+\cos\frac{5\pi}{6}}$

9. $\sec^2{x}+1=5$

10. $\ln[-\cos(4x)]=0$