Math 2200-01 (Calculus I) Spring 2020 Book 2 Sec 3.6 # 24 Ime . - PowerPoint PPT Presentation

Math 2200-01 (Calculus I) Spring 2020 Book 2

Sec 3.6 # 24 Ime . / * Itt ± - 49ft 19 . let S th = t 24.5 OE t s 5 , . height of the stone above the at time t ( in ground in meters , seconds ) . (a) vets = 5th = - 9.8T t 19.6 oft as is the initial height ; Note , slot = 24.5 m . ( in w/ see ) In His problem , Velocity at : time t is the initial velocity ✓ 107=19.6 nfsec . . positive direction being upwards motion is vertical with the the the moment when the velocity changes sign from positive its highest point . reaches The stone at (b) instantaneous velocity Solve ( downwards ) At this moment the negative ( upwards ) to zero is . . find t - 9.8ft 19.6=0 to vet ) 2 Sec - = - . (c) The maximum height = 44 . t sky is on The stone strikes the ground . - 4.9 ( E - 4T - 5) - 4. at 't 19.6 t t 245=0 when (d) sit ) = = t ) - 4.9 It - 5) Lt t =

This as the time when has two roots must have t = t = - I since t > o But 5 see , 5 see we the ground . , hits stone the . the ground with velocity downwards at a speed of The stone - 29.4 mlsec ( ie let hits v (5) = . m ( see ) 29.4 . time interval seconds speed 2 - t a 5 If , during the is increasing . - 9.8 my sea Reward is constant ' Cti ' ' acts = v et ) = s - - . Sec37ChainR dah Eg . find , since ' ) . In general = glhf xD and f- Cx ) if we know how do we find f ' ? ' ' , h g , other words a- dependent variable if In × tht u TF , an example - ex , think of As - sin u , y u - - independent variable ( intermediate variable small changes by rise to small changes Au small changes in y giving in u Dx give in x , . = Fff . 1¥ This refers to average rates of change To get instantaneous DI rates . of change , Det Dx → o . Au → o and Ay , giving ⇒ o so . Eh = hut d¥i , , ✓ Man 3

dah Eg ' e' , since cos ( e " ) ' ) = . U - ex - y - sink ) = Sinn x - - - Az = G- LT " ) ' . ex e' code cos u = = ~ - dye du Thi du Fx ( x 't 3 × 4+3 × 717 , ( x 't 15 dah Eg 6 × 5 t 12 × 3 t Gx ( OLD WAY ) = = . da . " " ? . :* ? ' i' ¥ , . :c :# ' : " : : . agrees . Rewriting this function notation × ↳ u= × I , I y= = 1 × 773 in u ' : = gchlx ) f- ( x ) ) - 31 × 715 ' f hlx ) = x' ti = g . 2x ' cha ) h' ( x ) f Cx ) = w - h 't x ) = 2x glu ) h' Cx ) u ' glu ) = g' cus =3 u '

hlx )= flglx ) ) (a) h' Ix ) = ' f- g' ( x ) Cg h' ( if F' ( gas ) g 'll ) = f' (4) = 7.9=63 - 9 . (b) him -_ f' Cgczs > g 'm = f' C , ) = f- 6) 7- = - 7 - 42 (c) h' (3) = fig k 's )=g4gG ) ) gt3 ) g 's ) Cd ) kex )=gcgC × D ( e ) = 9457.3 = f 't ) - 3=2.3 =6 K' g 'CgcxDg' Cx ) Cx ) = k 'll ) = gilgai ) gli ) - 5-3 -15 = = H ) hits ) - g 'lgl5Dg' Cs ) - 9=-1.9 = - g = g' (3) C- 5) g' (4) 3. f- 5) = -15 . = = day @ in x )lsiux ) dah ( OLD WAY ) sinxcosxt cost six Eg , sinx 29in x cos x = = = . dah da ( sinx )Z , sink ( NEW CHAIN RULE ) 2 sinx WAY cos x = = - ,

. *tD?;E - YETI as 13¥ ) da cos C sin C 3¥ . ) = = , , cos 13¥ s III. . ) =