Category Archives: Calculus

Calculus, Math

Stewart – Calculus – 1.6 – Inverse Functions and Logarithms

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  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
Calculus, Math

Stewart – Calculus – 1.3 – New Functions from Old Functions

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  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.

Calculus, Math

Stewart – Calculus – 1.2 – Mathematical Models

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  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.