Review. I will give you these formulas: Sphere: V=frr Circle: A = rr2 Cone: V = I 2rr2h Cube: V = side3
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1 You eed to kow: Rolle s Theoem: f ) f is cotiuous o [.bj, 2) f is diffeetible o (,b), d ) f()=f(b), the thee s oe c i (,b) whee f (c) = Me Vlue Theoem: l) f is cotiuous o [.b d 2) f is diffeetible o (,b), the thee s t lest to of the ldde isig t the momet the bottom is 5 feet fom the wll? icesig whe the dius is 6 iches? llel to the goud d t the te of feet e secod. At wht te must the stig be let out whe the legth of stig ledy let out is 2 feet? movig t costt te of feet e miute, is feet fom the fiish lie whe the he wkes u 5 betwee the thid bselie d the lie of sight fom the umie to the ue. How fst iso chgig whe sechlight tht ottes so s to lwys illumite the helicote. At how my dis e secod is the sechlight ottig whe the distce betwee the helicote d sechlight is 5 feet? d the to of the cu hs dius of 2 iches, how fst is the wte level isig whe the wte is 2 iches fom the wil, the bottom is beig ushed towd the wll t the te of Vz x feet e secod. How fst is the dee? goud? (The distce s fom the bll to the goud t secods fte elese is give by s = 66?.) feet fom the fiish lie d dts off fte the totoise. Let x be the distce fom the totoise to the fiish lie d, d suose the distce y fom the he to the fiish lie is give by y = 525J x. the ue is feet fom thid bse? but 5 feet fom the light. How fst is the shdow isig log the goud whe the bll is 5 feet fom the. A kite feet bove the goud is beig blow wy fom the eso holdig its stig, i diectio 6. A bsebll dimod is sque with sides 9 feet log. uose bsebll lye is dvg fom kecod b) Who wis d by how my feet? to thid bse t the te of 2 feet e secod, d umie is stdig o home lte. Let be the gle. A sheicl blloo is iflted t the te of cubic iches e miute. How fst is the dius of the blloo t lest oe c i (,b) whee f (c) =. 2. A ldde 5 feet log les gist veticl wll. uose tht whe the bottom of the ldde is x feet. Wte is oued ito coicl e cu t the te of /2 cubic iches e secod. ifthe cu is 6 iches tll 5. The totoise d the he e hvig thei fbled footce, ech movig log stight lie. The totoise, ) How fst is the he movig whe the totoise is feet fom the fiish lie? 7. A steet light 6 feet high csts shdow o the goud fom bll tht is doed fom height of 6 feet 8. A helicote feet high is movig hoizotlly t the te of feet e secod. t flies diectly ove will give you these fomuls: hee: V=f icle: A = 2 oe: V = 22h ube: V = side Review
2 Fid y ticl umbes of the fuctio. 9. f(x)=x6x29x. g(x)=x. k(t)=2tt 2. f(z)=zjz+ Detemie the bsolute extem of the fuctio d the xvlues i the closed itevl whee they occu.. f(x)=x25x6 [%,6J. g(x)= (,] 5. f(x)=x [,8] 6. f(x)=esc(x) [/8,%] 7. g(x)=/ [,] 8. hq=t [,5) Detemie whethe Rolle s Theoem c be lied to f o the idicted itevl. f Rolle s Theoem c be lied, fid ll vlues of c guteed by the theoem. 9. f(x) = x2 x+2 [,2) 2. f(x) = (x)(x+fl2 [,) 2. f(x)=x [,6] 22. f(x)=x [,] 2. f(x)=cosx [,2z] Aly the Me Vlue Theoem to f o the idicted itevl. ech cse, fid ll vlues of c guteed by the theoem. 2. fc)=xc2x2) [,) 25. f()=±fl [%2] 26. f(x)=x [o,i) 27. f(x)=2six+si2x [,z] 28. fg)=(x+j [,] 29. A g c cceleted fom test, tvelig 2 feet i 2 secods. Must the c hve bee tvelig t lest mh t some momet duig tht time itevl? xli. (Hit: ovet to miles d hous.)
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