Math1011_Week08

Math1011_Week08 - Math1011 Section 3.2 Use the definition...

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Math1011 Section 3.2 10/11/2010 Use the definition of the derivative to determine if the following function differentiable at x = 0? f ( x ) = x
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Math1011 Section 3.2 1 Use the definition of the derivative to determine if the following function differentiable at x = 0? f ( x ) = x 0 00 0 Let's use the definition of the derivative at 0 () ( ) '( ) |0 | |0| | | '(0) Let's look at the limit from the left, and the limit from the right || from the left, n lim lim lim lim h hh fx h fx fx f →→ →− +− = == 0 0 0 umbers are negative so |h|= - h 1 from the right, numbers are positive so |h|= h 1 Since the limit from the left differs from the limit from the right the limit does not lim lim lim →+ =− = h0 exist, so f'(0) = lim = DNE Thus, f (x) is NOT differentiable at x = 0 (Doc #1011w.32.02)
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Math1011 Section 3.2 2 Use the definition of the derivative to determine if the following function differentiable at x = 0? 0 () 10 xx fx = +>
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Math1011 Section 3.2 2 Use the definition of the derivative to determine if the following function differentiable at x = 0? 0 () 10 xx fx = +> 0 0 Let's use the definition of the derivative ( ) '( ) Let's look at the limit from the left, and the limit from the right From the left (0 ) 0 so use ( ) (thus (0 ) ) (0 ) ( lim lim h fx h fx hfx x f fh →− +− = +< = += 00 0 0 0 0) (0) 0 = 1 From the right (0 ) 0 so use ( ) 1 (thus (0 ) 1) ( 0)( 0 ) (1 )( 0 ) 1 0 1 = Since the limit from the left di lim lim lim lim lim lim lim hh hf →+ −− == = = + + + + + = ffers from the limit from the right the limit does not exist, so f'(0) DNE Thus, f (x) is NOT differentiable at x = 0 (Doc #1011w.32.03.doc)
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Math1011 Section 3.2 3 Given the graph of ƒ, sketch ƒ ‘
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Math1011 Section 3.2 3 Given the graph of ƒ, sketch ƒ ‘ (Doc #1011w.32.03)
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Math1011 Section 3.4 4 Water is flowing into a large hemispherical
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Math1011_Week08 - Math1011 Section 3.2 Use the definition...

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