Tangent Line Approximation / Linearization

Example:

Use a linear approximation to approximate the valve of each of the following:

a) sin(18π/17)

b) √15.9

Basic idea of Newton's Method and how to use it.

One example using Newton's Method to approximate a root. Example:

Find where f(x) = x

Example:

Compute two iterations of Newton's method for the given function and indicated initial guess:

f(x) = x

Example:

Apply two iterations of Newton's method to approximate the x-value of a point of intersection of these two functions using the given initial guess:

f(x) = x

What is the value of x

Example:

Given the following equation and initial guess, why would Newton's method fail to approximate a solution?

f(x) = (x - 2)

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