5.4 Completed Notes.pdf - 2 f'aCOrItinuosf(no...

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Unformatted text preview: 2!! f'aCOrItinuosf (no TheFundamental Theorem fo'Caiculus A. Fundamental Theorem of Calculus — Part I _ .-.. on the-intefval [agb], and g(x)_:' If“) dfw' '13" Reminder: Leibniz Notation %|: ‘_——.k :11 H V & I—J ‘iEVaria'tidris Oin'therrule': ' Examples: . d x 1. -— = ' ) dxhcostdt] COSX 2.)—c—i—j£l+x/9—t2dt]= 1+ ‘I-vx 107 (9 WW" Deslré Taylor Math 1242 mam/Edi] (m (“5’0“ \/Xt*5 '2" L) Desiré Taylor Math 1242 r ."'\ ‘\.../ 7.) Find the derivative of the functionf(x) alcosezfii . tlAnd do not forget to label!) :_- (04(2):?) :2 ’- COSCCQ’WeK 2 Emir. B. Average Value of a Function Example: [a b] l Webwor-|< x t2 _ 36 Gal/‘24» 1.. 5. (l pt)‘Given fix) 2 A l+cos'2(1) “1 .Atwimtvalue of 3: does the local max of fix! occm? > p {5%}: 0 ,73? r 'vac-a-J; S XWJJ g; 0 4:4 :g a l+C0$z£t) l+:o::x M“? X L30 L 1-, >11'C05 2% l 41:: six / \\ ++ r — _. : Xe" 5‘9 5 0 M3 Deslré Taylor 4- Math 1242 l L *6 ._ (a X 7:" {P MU lawnmm=£P+W+mmmmflm= My)? 0de LS tam?” 4*] T X3+7X¢+b puéx): 338* 114% 8. (1. pt.) Find a function f and a number a such that Y. if x<--S f0) : f5”"“"i?"“"‘1”§"§x"36f ' W 0 if x25 and gm : [5mm Determine the value of each of the l’olEowing: (mm—m=Q:$—-———————-—-=h-—u (b) g(—4) = — (C) 3(1) = (6) 3(6) = — . (e) The absolute maxinmm of g(x) occurs When x = _ and is equal to M - Desiré Taylor ...
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