12.05 - By request: Consider the function { x if x is...

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Unformatted text preview: By request: Consider the function { x if x is rational, f ( x ) = { { – x if x is irrational Where is it continuous? Even worse: the function { x 2 if x is rational, g ( x ) ={ { – x 2 if x is irrational is differentiable at 0 but nowhere else! Section 13.4: We did this in class a couple of weeks ago, but let’s do it again in case you’re rusty: Let D be the square with vertices ( ± 1,0) and (0, ± 1), and let C = ∂ D [draw sketch]. Find ∫ C ( x 4 +2 y ) dx + (5 x + sin y ) dy . ..?.. ∫ C ( x 4 +2 y ) dx + (5 x + sin y ) dy = ∫ ∫ D [ ∂ (5 x + sin y )/ ∂ x – ∂ ( x 4 +2 y )/ ∂ y ] dA = ∫ ∫ D [5 – 2] dA = ∫ ∫ D 3 dA = 3 times the area of D = 6. Group Work problem: Find the area under one arch of the cycloid with parametric equations x ( t ) = t – sin t , y ( t ) = 1 – cos t with 0 ≤ t ≤ 2 π . Hint: Use a formula from equations (5) from section 13.4....
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This note was uploaded on 02/13/2012 for the course MATH 241 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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12.05 - By request: Consider the function { x if x is...

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