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Wxhؕ="6 3ZlZF~fu-ԙՍh9 `aMD/`u8kpHvbp.H#Iy[ )V+qki,N*k,a{]GK:oO#KtZզ|1o1NR7pI+ad6Y>f+WM:\YX/(ԁTHedCLe!ʿ^6B L Z2_]ѶY)SE ЈMP}*Twjf-Yҕo ΎcF8+:ELpDž $V)Q Ua?SE'pehp+0P*F hLh{Ye_C朥aN~ꀆHP؏T$هdbl$YFDTI\ZG䐰zoPnIV dYBͩ!ks|l2Rn6 MnBĊ]ծ7󽷬Y<+Yi+hei"skAf.xqQc,.~>_):P[|t l iG8AL5m:iw֒4vќ\Hcgvlmǖ<{2Eahdc(>zށ)S|_ZρH~, PK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6 +_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-! 9\theme/theme/theme1.xmlPK-! ѐ' theme/theme/_rels/themeManager.xml.relsPK] :   { c (  "  lQ1?Text Box 13PJ 3.9 Linear Approximations*C<C<  |  DA ??Object 14"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDOˊ0 C;M,RE3>她Mi2f10yI+-+M#ę% kˤEpDێy!TPx$R nj=lkR؅pSy`ɡve(Yw8V]okƣ~?I+g07 O@n>PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK q 8 $D }  DA ??Object 15"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!O]drs/downrev.xmlDъ0Dp}[SEV⫶pim)Mlo9lEG,+N"Ĺ <2)xnD۞|!] JDJdMlCm B7EQ, VJlXR=>؞YcˮOWx8l@x'n_xXPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!O]drs/downrev.xmlPKN /8 $D  f3"V+Nf___PPT10+~Dg' = @B D"' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BBB B%(D' =1:Bvisible*o3>+#.<*%(D' =-o6Bbox(out)*<3<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+#.<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*+"y    (  t  j1?Text Box 2V  6Ex 1: a) Find the linearization of f(x) at x = 1.b77$7777777 7 ~  BA ??Object 3"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!"drs/downrev.xmlDOk1BCxoUd-[‚A꟞fiݤA8oŪwV gqZa_@z&W Z Xh/:b-C Lm!e 9 c';1ɮK;+YK -}~vN<[mjzRZx ,NrPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!"drs/downrev.xmlPKAg8 $D y  BA ??Object 4"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDO˪0 C5A6ҤY./j\iYl ά.9Wp'K#k,79ج&v|WsB%NtYAāƠɥn ᦒ(CC5 ʞikPzs{i޺ OVq+ PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK d8 $D    j`1?Text Box 5  .b) Then use it to approximate the following: / /< /  f3"V+Nf  ___PPT10 +mD ' = @B Du ' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+#.<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+#.<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*+"  0(  h  j1?Text Box 2 3  VEx 1: c) For what values of x is the linear approximation accurate to within 0.5?6W77777 W  f3"V+Nfy___PPT10Y+D=' = @B +" P y(     j@1?Text Box 2kZ w Differential:( C<C<  ~   BA ??Object 32"  ~   BA ??Object 4 Y    ~ Ao?Rectangle 5S\:  N     j@B1?Text Box 6q! ~3.9 Differentials*C<C<   f3"V+Nfy___PPT10Y+D=' = @B +"5 4,p(    j@1?Text Box 2P ,$ dy represents the amount that the tangent line rises/falls. Dy represents the amount that the curve (i.e. secant line) rises/falls.<< < <<<<< <<< < <<   f3"V+Nfy___PPT10Y+D=' = @B +"  (     vA??[image]Picture 3[image]YmIB  h>?Line 4p B  h>?Line 5 ii 2  # zM1?Oval 6- N   2  # z`O1?Oval 7;C N   2  # z 1?Oval 8;. N   2  # zyQ1?Oval 9#; N   B  j>?Line 10WsWB  j>?Line 110ioF  r@1?Text Box 122Q M _P #    r`1?Text Box 13] _Q #    r1?Text Box 16T `dy #3    r1?Text Box 17XT tDy. #f#f    r1?Text Box 18 NN 4 _x #  .  r1?Text Box 19 N&  x + Dx> ###   r  3 Gio?AutoShape 20;B  N   0  r 1?Text Box 21)   dx = Dx> ###  B   pf)?Line 22   # G 3Ԕ?AutoShape 15V N      `fԔ?AutoShape 14hQ N    f3"V+Nfy___PPT10Y+D=' = @B +" $j(  $2 $ j G1?Text Box 2dm,$ dEx 2: Compare the values of Dy and dy if y = f(x) = x3 + x2  2x + 1 and x changes from 2 to 2.05. Z^<<<<<<<<<<<<<<<<<<<<< <<<< e  f3"V+Nfy___PPT10Y+D=' = @B +"' ((  ( (  xG0e0e?Rectangle 2[n    \HW  3.9 pg. 240 # 1  25 odds, # 43  47 odds(/ .<< / f3"V+Nfy___PPT10Y+D=' = @B +  ,n(  ,6 , j`I1?Text Box 2"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!Mdrs/downrev.xmlDKk1Cj2(VvW|ɝ1$q\7_F|蜕M0Sm$7`!U% 7 \LX*w;a bCPd0L]O6uc57bO떪b$c?0~r_|8|yW"|NC$(՟ߩH^BKPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!Mdrs/downrev.xmlPK ,$ Read Apps to Physics pg. 262"77   f3"V+Nfzr___PPT10R+G9rD' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+#.<*,%(D' =-o6Bdissolve*<3<*,+8+0+, +"v  |t0\(  0$ 0 j`F1?Text Box 2"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!pUdrs/downrev.xmlDN0EH5H쨝 E([AP+P~OdXrtG޳fL!NJީ*Β En(w4A cJ<# ɖT0p\F5780vse$cgaN-Cinɏ+`rk_zUjq_GT1QPm1PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!pUdrs/downrev.xmlPK V P,$ pEx 2: Suppose that after stuffing a turkey its temp is 50 F & you put it in a 325 F oven. After 1 hr. the turkey is 93 F & after 2 hrs. the turkey is 129 F. 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