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Examples
Lessons
1. Approximating values using Quadratic Approximations

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

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

The formula for quadratic approximation is:

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

Where:

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

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