# 4.5 - x = π 2 Calculus Section 4.5 Page25 b How accurate...

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Calculus Section 4.5 Page 24 4.5 Linearization Linear Approximation Exploration Approximating with Tangent Lines Let f x ( ) = x 2 . 1. Show that the line tangent to the graph of f at the point 1, 1 ( ) is y = 2 x - 1. 2, Set y 1 = x 2 and y 2 = 2 x - 1. Zoom in on the two graphs at 1, 1 ( ) . What do you see? Definition Linearization If f is differentiable at x = a , then the approximating function L x ( ) = f a ( )+ f a ( ) x - a ( ) is the linearization of f at a . Example 1 a) Find the linearization L x ( ) (or linear approximation) of f x ( ) = 1 + x at x = 0 . b) How accurate is the approximation L 0 + 0.1 ( ) ≈ f 0 + 0.1 ( ) for values of x near 0? Example 2. a) Find the linearization L x ( ) of f x ( ) = cos x at

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Unformatted text preview: x = π 2 . Calculus Section 4.5 Page25 b) How accurate is the approximation L π 2 + 0.1 ≈ f π 2 + 0.1 for values of x near π 2 ? Definition Differentials Let y = f x ( ) be a differentiable function. The differential dx is an independent variable. The differential dy is defined as: dy = ′ f x ( ) dx Example 3. Find dy and evaluate dy for the given value of x and dx . What does this mean geometrically in a)? a) y = x 2 x = 1, dx = 0.01 b) y = x 1-x 2 x = 0, dx = -0.2 Assignment III-5 Pages 229 – 230 #1 – 5 all, 19, 21, 23...
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4.5 - x = π 2 Calculus Section 4.5 Page25 b How accurate...

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