# Calculus Exam 2 Review

Velamur Quiz 7

Velamur Quiz 8 *Note: Inflection points are not on Exam 2.

Velamur Quiz 9 *Note: Inflection points are not on Exam 2.

# Trigonometry Test Review Solutions

1.
a. $\frac{\sqrt{2}}{2}$

b. $\frac{\sqrt{3}}{3}$

c. -1

d. -2

e. -1

2. 45

3. $\frac{-13}{12}$

4. unknown angle is 43 degrees, unknown sides are 18 feet and 13 feet

5. 39

6. The fire is 182.3 miles from station A and 128.7 miles from station B.

# more triangle trigonometry questions

1. Calculate the area of a regular octagon inscribed in a unit circle.
2. In quadrilateral ABCD, AB=3, BC=4, CD=5, and DA=6. The length of diagonal BD is 7. Calculate the length of the other diagonal.
3. From the top of an observation post that is 90 meters high, a ranger sights a campsite at an angle of depression of 10°. Turning in a different direction, the ranger sees another campsite at an angle of depression of 13°. The angle between these two sight lines is 35°. How far apart are the campsites?

# Trigonometry Test 2 is on Tuesday!

There are 14 questions, broken down as follows.

3 graphing rational functions

2 simplifying logs

3 log equations

2 exponential equations

1 inverse function

1 graphing exponential function

1 graphing log function

1 write the equation of an exponential function given certain conditions

Here are some good review questions.

1. Solve for $x$: $\log_5(2x)=\log_5(x+1)-1$
2. Solve for $x$ and express your solution as a ratio of natural logs: $3^{\frac{-x}{2}}=4^{x+1}$
3. Sketch the graph of $f(x)=-\ln(x-4)+2$
4. Sketch the graph of $f(x)=e^{\frac{-x}{3}+1}$
5. Sketch the graph of $f(x)=\frac{(x+2)^2(x+1)}{(x-4)^3(x-6)}$
6. $f(x)$ has a horizontal asymptote at $y=5$. Where is the asymptote for $f^{-1}(x)$?
7. $f(x)=-5^x+1$. Write the equation for $f^{-1}(x)$.
8. Solve for $x$ and express your solution as a ratio of natural logs: $3^x+2=10$.
9. Re-write as an exponential equation: $\log_{64}4=\frac{1}{3}$.
10. Sketch the graph of $f(x)=\frac{6x^2+19x-7}{2x+7}$

Also study quizzes 2, 3, and 4.

# Critical vocabulary for midterm

Can you define all these terms? Doing so should be excellent practice for the exam, as well as a chance to review topics we’ve focused on over the past six weeks.

Rational function

Exponential function

Logarithmic function

Asymptote

Zeroes

y-intercept

Logarithm

Inverse function

Logarithmic scale

Exponential growth

Exponential decay

Exponential growth rate

Exponential decay rate

Continuously compounded interest