AP Calculus AB First Semester Final Review

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1 P Clculus B This review is esigne to give the stuent BSIC outline of wht nees to e reviewe for the P Clculus B First Semester Finl m. It is up to the iniviul stuent to etermine how much etr work is require for concept mstery. Chpters n. Stte the omin of functions (p. # 7-3). Re limit vlues from grphs (p. 96 # 4-9) Left-Hn Limits Right Hn Limits Unerstn tht f() vlues cn eist ut tht the limit t oes not hve to. 3. vlute limits. Be sure you know the fctoring techniques covere in clss. (p. 7 # s -7, 39-43) 4. vlute limits tht pproch infinity (horizontl symptotes): lim f() = L (p. 4 # s 5-9, 3, 3, 39-43) 5. Be le to ientify n lel iscontinuities from grphs. Don t forget out the 3-step process to prove tht prticulr -vlue ( = ) is iscontinuity. ). ƒ() eists ). lim ƒ() eist (Rememer to check the left n right-hn limits) 3) lim ƒ() = ƒ() 6. Be le to grph piecewise function n ientify ny iscontinuities using the 3-step metho (p. 8 # s 5-) 7. Re grph n stte where the function is NOT DIFFRNTIBL n why. (p. 64 # 35-38) Kinks, corners, iscontinuities, n enpoints! Chpter 3. Bsic Rules of Differentition: (pg s 73-8) n (pg s 83-87) n (pg 93) (constnt) = (n ) = n () (n-) Cƒ() = C ƒ() e = e (ƒ()g()) = g() ƒ () + ƒ() g () f( ) g ( ) = g() ƒ () - ƒ() g () [g()] sin() = cos() sec() = sec()tn() cos() = -sin() tn() = sec () csc() = -csc()cot() cot() = -csc (). Slope of tngent line = ƒ () (p. 8 # s 33, 35) Given prticulr function fin the eqution of the tngent line y y = m(- ) t given point P(, f()) where (, y ) = P(, f()) 3. Given position function, s(t), e le to clculte the velocity n ccellertion of prticle t t = (p. 8 # 49) First Semester Clc B Chpters -5 Finl Review

2 (csc (cos (sec (tn (cot P Clculus B This review is esigne to give the stuent BSIC outline of wht nees to e reviewe for the P Clculus B First Semester Finl m. It is up to the iniviul stuent to etermine how much etr work is require for concept mstery. Chpter 3: Continue 4. Chin Rule: (pg 97) y = y u u 5. Implicit Differentition: (pg s 3 # s 5-5 o, 5) 6. Derivtives of Logrithms: (pg s pg # s -9 o) log() = ln() [ln(g())] = g'() g() ln() = ln = Logrithmic Differentition: You MY wnt to use this if you re hving troule tking the erivtive of prticulr function.. Tke the nturl logrithm of oth sies n simplify using the properties of logrithms.. Differentite Implicitly (with respect to ). 3. Solve for y. 7. Derivtives of Inverse Trig. Functions: (pg 4 # s o) (sin- ) = (rcsin ) = - - ) = (rccsc ) = ) = (rccos ) = ) = (rcsec ) = - - ) = (rctn ) = + - ) = (rccot ) = Rtes of Chnge: (p. 3 # s, 3) 9. Relte Rtes (p. 45 # s -6, -4,, 3) First Semester Clc B Chpters -5 Finl Review

3 or P Clculus B This review is esigne to give the stuent BSIC outline of wht nees to e reviewe for the P Clculus B First Semester Finl m. It is up to the iniviul stuent to etermine how much etr work is require for concept mstery. Chpter 4. Section 4.: Mimum n Minimum Vlues (p. 77) Locl Mimums/Minimums Cnnot occur t the enpoints of the omin Horizontl sections re oth locl m/min (ecluing the enpoints) solute Mimum/Minimums The lrgest y-vlue = solute M The smllest y-vlue = solute Min Cn occur t the enpoints of the omin Criticl Numers = c ƒ () = or ƒ () D.N. The Close Intervl Metho: To fin the solute m n solute min vlues of continuous function ƒ on close intervl [, ]. Fin the criticl numers n clculte ƒ(c). Fin the vlues of ƒ t the enpoints of the intervl. solute M Vlue = Lrgest ƒ-vlue solute Min Vlue = Smllest ƒ-vlue. Section 4.: Rolle s n The Men Vlue Theorem (p. 85) Rolle s Theorem: If ƒ is function tht stisfies the following three hypotheses:. ƒ is continuous on the close intervl [, ].. ƒ is ifferentile on the open intervl (, ). 3. ƒ() = ƒ() Then there is numer c in (, ) such tht ƒ (c) = Men Vlue Theorem: If ƒ is function tht stisfies the following hypothesis:. ƒ is continuous on the close intervl [, ].. ƒ is ifferentile on the open intervl (, ). Then there is numer c in (, ) such tht ƒ() - ƒ() ƒ (c) = equivlently ƒ() - ƒ() = ƒ (c)[( )] - 3. Section 4.3: How Derivtives ffect Grph (p. 95) Given ƒ() you shoul e le to: i). Fin the intervls on which ƒ is incresing or ecresing You o this y uiling tle n using the ID Test. ii). Fin the locl m n locl min vlues of ƒ. You o this y reing the sign chnges in the tle you uil for step i). This is the st Derivtive Test. iii). Fin the points of inflection n intervls of concvity. You o this y tking the secon erivtive n evluting where ƒ () = or D.N.. These re possile points of inflection. You then uil nother tle n re the signs of ƒ (). This will lso vlite ny possile POIs. 4. Section 4.4: L Hospitl s Rule (p. 34) Only works for limits tht re ineterminte : ± Cn e use multiple times if the new limit stisfies the ove step! 5. Section 4.7: Optimiztion Prolems (p 38) First Semester 3 Clc B Chpters -5 Finl Review

4 P Clculus B This review is esigne to give the stuent BSIC outline of wht nees to e reviewe for the P Clculus B First Semester Finl m. It is up to the iniviul stuent to etermine how much etr work is require for concept mstery. Chpter 5: Integrls 5. pproimting The re Uner Curves (p ) Left-Hn, Right-Hn, Mipoint n = numer of su-intervls 5. The Definite Integrl (p ) n Riemnn Sum = f( i ) i= n f( ) = lim f( i ) where i = left-right-mipoints n i = Specil Cses with Definite Integrls: o f ( ) = o f ( ) = f ( ) = Properties of Integrls on pge Funmentl Theorem of Clculus Prt I: Unerstn tht: u() o If g() = f(t)t = The re Uner the Curve o Then, g () = f(u()) u () Prt II: You shoul e le to know how evlute integrls (with ounries) Inefinite Integrls n the Net Chnge Theorem [ f ( ) + g( )] = f ( ) + g( ) cf ( ) = c f ( ) k = k k =constnt n+ n = (n -) ln C n + = + e = e = ln sin( ) = cos( ) cos( ) = sin( ) sec ( ) = tn( ) csc ( ) = cot( ) sec( ) tn( ) = sec( ) csc( )cot( ) = csc( ) tn ( ) rctn( ) + = = = sin ( ) = rcsin( ) The Net Chnge Theorem: Rte = The Net Chnge Velocity = Displcement Velocity = Totl Distnce Trvele First Semester 4 Clc B Chpters -5 Finl Review

5 P Clculus B This review is esigne to give the stuent BSIC outline of wht nees to e reviewe for the P Clculus B First Semester Finl m. It is up to the iniviul stuent to etermine how much etr work is require for concept mstery. ssingment List Chpter n : Pge 74 # s 5-8 (omin only) Pge 67 # s, 3-9 o, 3, 7, 43 Chpter 3 Chpter 4 Shoul know pge 6 Concept Check # Pge 6 ercises # s -5 o,, 57, 59, 6, 83, 89, Pge 45 # s, 3, 7 Pge 85 # s, 3,, 3 Pge 95 # s,, 33, 4 Pge 38 # s 9, 3, 9 Pge 348 ercises - o, 8 Chpter 5: Pge 49 # s, 9-9 o, 3, 5, o, 56 First Semester 5 Clc B Chpters -5 Finl Review

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