Quadratic approximation

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Intros
Lessons
  1. Quadratic Approximation Overview

    What is quadratic approximation?

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Examples
Lessons
  1. Approximating values using Quadratic Approximations

    Find the Quadratic approximation to the function at the given point:

    1. f(x)=2cosxf(x) = 2\cos{x} at a = π2\frac{\pi}{2}
    2. g(x)=x3+2x2+5x+4g(x) = x^{3} + 2x^{2} + 5x + 4 at a = 1
  2. Consider the function f(x)=xf(x) = \sqrt{x}
    1. Find the quadratic approximation of the function at a=4a = 4
    2. Approximate 5\sqrt{5} and 6\sqrt{6}
    3. Compare the exact values of 5\sqrt{5} and 6\sqrt{6} with your approximated values in part b). How close were we?
  3. Approximate ln2\ln{2}
    Topic Notes
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    The formula for quadratic approximation is:

    Q(x)=f(a)+f(a)(xa)+f(a)2(xa)2Q(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2}(x - a)^{2}

    Where:

    f(a)+f(a)(xa)f(a) + f'(a)(x - a) is the linear part

    f(a)2(xa)2\frac{f''(a)}{2}(x - a)^{2} is the quadratic part.

    Basic Concepts
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