# Stewart – Calculus – Appendix D – Trigonometry

1. Fill in the missing steps.

2. By what must you divide

in order to get
?

3. Complete the identity expressions.

4. Complete the identity expressions.

5. Complete the identity expressions.

# Stewart – Calculus – 1.6 – Inverse Functions and Logarithms

1. Can two different numbers have the same cube?

2. Find the inverse of the equation

3. Find the inverse of the equation

4. True or false:

is equal to
.

5. Solve.

6. Find the inverse function of

7. What is the inverse of the equation $log _{a}x=y$?

8. Find equivalent equations.

9. Find the equations that correspond to the labels.

10. Find equivalent forms.

11. Use the laws of logarithms to evaluate $log_2{80} - log_2{5}$.

12. Find the equivalent natural log.
$log_e{x}$
13. Find the equivalent equation for ln x = y.

14. Find the equivalent forms.

15. Solve the equation
.

16. Express $\ln a+\frac{1}{2}\ln b$ as a single logarithm.

17. The change of base formula says that
For any positive number $a(a{\neq}1)$, we have $log_a{x}=$.

18. Sketch the graph of the function $y=\ln (x-2)-1$.

19. Find the inverse of $\sin ^{-1}x=y$.

20. Evaluate $\tan (\arcsin \frac{1}{3})$.
No.
False.
1. Re-write the equation:
2. Solve this equation for x:
3. Interchange x and y:
4. So, inverse function is:
ln x
Let , so
Then we can draw a right triangle with angle θ as in the figure

and deduce from the Pythagorean Theorem that the third side has length

This enables us to read from the triangle that

# Stewart – Calculus – 1.5 – Exponential Functions

1. Find equivalent forms.

2. Sketch the graph of the function

and determine its domain and range.

3. Sketch the graph of the function

and determine its domain and range.

# Stewart – Calculus – 1.3 – New Functions from Old Functions

1. Find the equations that correspond to each letter on the following graph.

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2. Find the equations that correspond to each letter on the following graph.

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3. Find the equations that correspond to each letter on the following graph.

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4. Find the equations that correspond to each letter on the following graph.

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5. Find the equation that corresponds to the letter on the following graph.

# Stewart – Calculus – 1.2 – Mathematical Models

1. What does the following symbol mean?

2. What is the equation of the following graph?

3. Estimate the correct exponents in the following graph.

4. Find the correct exponents in the following graph.

5. Give the equation of the following graph.

6. Give the equation of the following graph.

7. Give the equation of the following graph.

8. Give the equation of the following graph.

9. Give the equation of the following graph.

10. Give the equation of the following graph.

11. Give the equation of the following graph.

12. Give the equations of the following graph.

13. Give the equation of the following graph.

14. Identify the function type.

all real numbers
y = x
A = 6, B = 4
A = 3, B = 5
Exponential function. (The x is the exponent.)
Power function. (The x is the base.) We could also consider it to be a polynomial of degree 5.
Algebraic function.
Polynomial of degree 4.