Chapter 3 Section 02

Chapter 3 Section 02 - Chapter 3 Section 02 Derivative as a...

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1 Chapter 3 Section 02 Derivative as a function
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2 Objectives: 1. Find the derivative of a given function using the definition of derivative. 2. Identify where a function is differentiable or nondifferentiable from its graph. 3. Find derivatives using the power rule. 4. Find derivatives using the exponential rule. 5. Find the slopes and equations of tangent lines.
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3 Definition h x f h x f x f h ) ( ) ( lim ) ( ' 0 - + =
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4 other notations [ ] ) ( ) ( ) ( ' ) ( ' x f D x f D x f dx d dx df dx dy y x f x = = = = = = D and D x and d/dx are called differentiation operators. dy/dx is not a ratio, but one quantity. (We will see it as a ratio later.) A function is differentiable at “a” if f’(a) exists. It is differentiable on an open interval (a, b) or (a, ∞) or (-∞, ∞) if it is differentiable at every number in the interval.
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5 x h x h h x h h h xh h x h xh x h x h x h x f h x f x f h h h h h h 2 ] 2 [ lim ) 2 ( lim 2 lim ] 2 [ lim ) ( lim ) ( ) ( lim ) ( ' x f(x) if (x) f' Find 0 0 2 0 2 2 2 0 2 2 0 0 2 = + = + = + = - + + = - + = - + = =
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6 x x h x x h x h h x h x h x h x x h x x h x h x h x h x h x h x f h x f x f h h h h h h 2 1 1 lim ) ( lim ) ( ] [ lim lim lim ) ( ) ( lim ) ( ' x f(x) if (x) f' Find 0 0 0 0 0 0 = + + = + + = + + - + = + + + + × - + = - + = - + = =
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2 0 0 0 0 0 0 1 ) ( 1 lim ) ( lim ) ( ) ( lim ) ( ) ( 1 1 lim 1 1 lim ) ( ) ( lim ) ( ' x 1 f(x) if (x) f' Find
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This note was uploaded on 09/28/2009 for the course MATH 1550 taught by Professor Wei during the Spring '08 term at LSU.

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Chapter 3 Section 02 - Chapter 3 Section 02 Derivative as a...

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