Category Archives: Calculus
Stewart – Calculus – 1.6 – Inverse Functions and Logarithms
- Can two different numbers have the same cube?
- Find the inverse of the equation
- Find the inverse of the equation
- True or false:
is equal to
.
- Solve.
- Find the inverse function of
- What is the inverse of the equation
?
- Find equivalent equations.
- Find the equations that correspond to the labels.
- Find equivalent forms.
- Use the laws of logarithms to evaluate
.
- Find the equivalent natural log.
- Find the equivalent equation for ln x = y.
- Find the equivalent forms.
- Solve the equation
.
- Express
as a single logarithm.
- The change of base formula says that
For any positive number, we have
.
- Sketch the graph of the function
.
- Find the inverse of
.
- Evaluate
.
No.


False.

- Re-write the equation:
- Solve this equation for x:
- Interchange x and y:
- 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



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
Stewart – Calculus – 1.3 – New Functions from Old Functions
- Find the equations that correspond to each letter on the following graph.
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- Find the equations that correspond to each letter on the following graph.
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- Find the equations that correspond to each letter on the following graph.
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- Find the equations that correspond to each letter on the following graph.
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- Find the equation that corresponds to the letter on the following graph.













Stewart – Calculus – 1.2 – Mathematical Models
- What does the following symbol mean?
- What is the equation of the following graph?
- Estimate the correct exponents in the following graph.
- Find the correct exponents in the following graph.
- Give the equation of the following graph.
- Give the equation of the following graph.
- Give the equation of the following graph.
- Give the equation of the following graph.
- Give the equation of the following graph.
- Give the equation of the following graph.
- Give the equation of the following graph.
- Give the equations of the following graph.
- Give the equation of the following graph.
- 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.