( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).


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1 AB Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 A3 Find the intersection of f ( x) nd g( x). Show tht f ( x) is even. A4 Show tht f ( x) is odd. A5 Find domin of f ( x). A6 Find verticl symptotes of f ( x). A7 If continuous function f ( x) hs f ( ) < k nd f ( ) > k, explin why there must e vlue c such tht < c < nd f ( c) = k. B. Limit Prolems B1 Find lim f ( x). x " This is wht you think of doing B2 B3 Find lim f x x " piecewise function. ( ) where f ( x ) is Show tht f ( x) is continuous. B4 Find lim f ( x) nd lim f ( x). x "# x "$# B5 Find horizontl symptotes of f ( x) Stu Schwrtz
2 C. Derivtives, differentiility, nd tngent lines C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 Find the derivtive of function using the derivtive definition. Find the verge rte of chnge of f on [, ]. Find the instntneous rte of chnge of f t x =. Given chrt of x nd f ( x) nd selected vlues of x etween nd, pproximte f "( c) where c is vlue etween nd. Find the eqution of the tngent line to f t ( x 1, y 1 ). Find the eqution of the norml line to f t x 1, y 1 ( ). Find xvlues of horizontl tngents to f. Find xvlues of verticl tngents to f. Approximte the vlue of f ( x 1 + ) if you know the function goes through point x 1, y 1 ( ). Find the derivtive of f ( g( x) ). This is wht you think of doing C11 C12 C13 The line y = mx + is tngent to the grph of f ( x) t ( x 1,y 1 ). Find the derivtive of the inverse to f x ( ) t x =. Given piecewise function, show it is differentile t x = where the function rule splits Stu Schwrtz
3 D. Applictions of Derivtives D1 Find criticl vlues of f ( x). This is wht you think of doing D2 D3 D4 Find the intervl(s) where f ( x) is incresing/decresing. Find points of reltive extrem of f x ( ). Find inflection points of f ( x). D5 D6 Find the solute mximum or minimum of f x ( ) on [, ]. Find rnge of f ( x) on ("#,#). D7 Find rnge of f ( x) on [, ] D8 D9 Show tht Rolle s Theorem holds for f x ( ) on [, ]. Show tht the Men Vlue Theorem holds for f x ( ) on [, ]. D10 Given grph of f "( x), determine intervls where f ( x) is incresing/decresing. D11 Determine whether the liner pproximtion for f ( x 1 + ) overestimtes or underestimtes f ( x 1 + ). D12 Find intervls where the slope of f ( x) is incresing. D13 Find the minimum slope of f ( x) on [, ] Stu Schwrtz
4 E. Integrl Clculus E1 E2 E3 E4 E5 E8 E9 E10 E11 E12 Approximte " f ( x) dx using left Riemnn sums with n rectngles. Approximte " f ( x) dx using right Riemnn sums with n rectngles. Approximte Riemnn sums. Approximte " f ( x) dx using midpoint " f ( x) dx using trpezoidl summtion. Find " f ( x) dx where <. Mening of Given x " f ( t) dt. " f ( x) dx, find " [ f ( x) + k] dx. Given the vlue of F ntiderivtive of f is F, find F( ). Find d dx Find d dx x " f ( t) dt. g( x) " f ( t) dt. ( ) where the This is wht you think of doing F. Applictions of Integrl Clculus F1 F2 Find the re under the curve f x the intervl [, ]. ( ) on Find the re etween f ( x) nd g( x). This is wht you think of doing F3 Find the line x = c tht divides the re under f ( x) on [, ] into two equl res Stu Schwrtz
5 F4 F5 F6 F7 F8 F9 Find the volume when the re under f ( x) is rotted out the xxis on the intervl [, ]. Find the volume when the re etween f ( x) nd g( x) is rotted out the xxis. Given se ounded y f ( x) nd g( x) on [, ] the cross sections of the solid perpendiculr to the xxis re squres. Find the volume. Solve the differentil eqution dy dx = f ( x )g( y). Find the verge vlue of f ( x) on [, ]. Find the verge rte of chnge of F " x [ ]. ( ) on t 1,t 2 This is wht you think of doing F10 y is incresing proportionlly to y. F11 Given dy, drw slope field. dx G. Prticle Motion nd Rtes of Chnge G1 G2 G3 G4 G5 G6 Given the position function s t prticle moving long stright line, find the velocity nd ccelertion. Given the velocity function v( t) nd s( 0), find s( t). ( ) of Given the ccelertion function t prticle t rest nd s( 0), find s( t). ( ) of Given the velocity function v( t), determine if prticle is speeding up or slowing down t t = k. Given the position function s( t), find the verge velocity on [ t 1 Given the position function s t ( ), find the instntneous velocity t t = k. This is wht you think of doing Stu Schwrtz
6 G7 G8 G9 G10 G11 G12 G13 G14 G15 Given the velocity function v( t) on [ t 1,t 2 ], find the minimum ccelertion of prticle. Given the velocity function v( t), find the verge velocity on [ t 1 Given the velocity function v( t), determine the difference of position of prticle on [ t 1 Given the velocity function v( t), determine the distnce prticle trvels on [ t 1 Clculte t 2 " t 1 ( ) dt v t without clcultor. Given the velocity function v( t) nd s( 0), find the gretest distnce of the prticle from the strting position on [ 0,t 1 ]. The volume of solid is chnging t the rte of The mening of # R "( t) dt. Given wter tnk with g gllons initilly, filled t the rte of F( t) gllons/min nd emptied t the rte of E( t) gllons/min on [ t 1,t 2 ] ) The mount of wter in the tnk t t = m minutes. ) the rte the wter mount is chnging t t = m minutes nd c) the time t when the wter in the tnk is t minimum or mximum. This is wht you think of doing Stu Schwrtz
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