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

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

 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.