Linear approximation

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Intros
Lessons
  1. Introduction to Linear Approximations
  2. What is a linear approximation?
  3. Linear Approximation – Lesson Overview.
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Examples
Lessons
  1. Apply Linear Approximations and Discuss How to Choose "a"
    Consider the function f(x)=x. f(x)=\sqrt{x}.
    1. Sketch the graph
    2. Find the linearization of the function f(x)=xf(x)=\sqrt{x} at a=4, a=4, and illustrate the tangent line on the graph.
    3. Use the linear approximation to estimate the numbers:
      i)
      4.084 \sqrt{4.084}
      ii)
      3.96 \sqrt{3.96}
      Are these approximations overestimates or underestimates?
    4. Use the same linear approximation to estimate the number 10.2 \sqrt{10.2} , and comment on the accuracy of the approximation. How can the approximation be improved?
  2. Linearization of Radical Functions
    Use a linear approximation to estimate: 68\sqrt{68}
    1. Linearization of Polynomial Functions
      Use a linear approximation to estimate: (2.01)6(2.01)^6
      1. Linearization of Rational Functions
        Use a linear approximation to estimate: 197\frac{1}{97}
        1. Linearization of Exponential Functions
          Use a linear approximation to estimate: e0.025e^{0.025}
          1. Linearization of Logarithmic Functions
            Use a linear approximation to estimate: ln0.98\ln 0.98
            1. Linearization of Trigonometric Functions
              Use a linear approximation to estimate: sin24°\sin 24 \degree