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Calculus

Linear approximation- Home
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Still Confused?

Try reviewing these fundamentals first

Calculus

Linear approximationStill Confused?

Try reviewing these fundamentals first

Calculus

Linear approximationNope, got it.

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Get Started NowStart now and get better math marks!

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Get Started Now- Intro Lesson3:50
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- Lesson: 38:56

Basic Concepts: Linear approximation

The formula for quadratic approximation is:

Where:

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

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

- IntroductionQuadratic Approximation Overview
What is quadratic approximation?

- 1.
**Approximating values using Quadratic Approximations**Find the Quadratic approximation to the function at the given point:

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