AP Calculus January 23, 2009

Page 1 <img data-url='document/ap-calculus-january-23-2009.html?page=1' data-page='1' class='cut-thumb lazyload' alt='Page 1: AP Calculus January 23, 2009' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021421/58edd3021a28ab76458b4569/html5/thumbnails/1.jpg' width='140' height='200' /> Antidifferentiating by Substitution

The Birth of Substitution

Page 2 <img data-url='document/ap-calculus-january-23-2009.html?page=2' data-page='2' class='cut-thumb lazyload' alt='Page 2: AP Calculus January 23, 2009' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021421/58edd3021a28ab76458b4569/html5/thumbnails/2.jpg' width='140' height='200' /> Substitution: The Big Idea ... an example ...

=

Substitute

Antidifferentiate

Resubstitute

Page 3 <img data-url='document/ap-calculus-january-23-2009.html?page=3' data-page='3' class='cut-thumb lazyload' alt='Page 3: AP Calculus January 23, 2009' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021421/58edd3021a28ab76458b4569/html5/thumbnails/3.jpg' width='140' height='200' /> Substitution ... when the pieces are all there ...

Page 4 <img data-url='document/ap-calculus-january-23-2009.html?page=4' data-page='4' class='cut-thumb lazyload' alt='Page 4: AP Calculus January 23, 2009' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021421/58edd3021a28ab76458b4569/html5/thumbnails/4.jpg' width='140' height='200' /> Substitution ... when the pieces are all there ...

Page 5 <img data-url='document/ap-calculus-january-23-2009.html?page=5' data-page='5' class='cut-thumb lazyload' alt='Page 5: AP Calculus January 23, 2009' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021421/58edd3021a28ab76458b4569/html5/thumbnails/5.jpg' width='140' height='200' /> Substitution ... when some pieces are missing ...

Page 6 <img data-url='document/ap-calculus-january-23-2009.html?page=6' data-page='6' class='cut-thumb lazyload' alt='Page 6: AP Calculus January 23, 2009' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader031.cupdf.com/reader031/viewer/2022021421/58edd3021a28ab76458b4569/html5/thumbnails/6.jpg' width='140' height='200' /> Substitution ... when some pieces are missing ...

AP Calculus January 23, 2009

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