Calculus Practice Worksheet

# Calculus Practice Worksheet - w N€‘ ‘ r" 3‘ P1...

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Unformatted text preview: w N€‘+‘--+r" 3‘: _ ___ - P1; 0m 1):)? r NAME CALCULUS “ DATE ’ CALCULUS PRACTICE WORKSHEET These are some of the problems that were in my AP Book as samples. I picked out the ones that I thought all of you should be able to do at this point. (or at least have a good idea of where to start.) They are from the multiple choice section of the test but I did not give you choices (conservation of paper and I thought you could do them on your own). I picked 15 of the 28 in the section. The time limit for the 28 is 55 minutes with NO CALCULATOR! Key points to remember: 1. Unless otherwise speciﬁed, the domain of a ﬁmction f is assumed to be the set of all Real numbers 3: for which f (x) is a Real number. 2. The inverse of a trigonometric function f may be indicated using the inverse function notation f’1 or with the preﬁx “are” (e.g., sin‘I x = arcsin x ). l.Ify=(x3+l)2,thenﬁnd “tzi’éwd‘g‘”; 2 8-4de :QGZLffSI—ldil‘D‘I 0375 \E‘:."_':". 1{:;F\: ‘ ' 2x+3 dy \{H{3'04'31942‘H3M33t’fﬁ :7“ 7: I +2 3.Ify= ,thenﬁnd—. t-” _c‘, A ﬁt! -‘lEf’ 3H2 dx 4:: blag-#7 : (35.9. 4 feltide -coe><]5§s “’i h '7 c I - “ . i—q _. A “ammo- 5 hm x3—2x2+3x—4 3( 3: 5: Z 6-. Ixz'cosbgldf 33 5059 “H” 3 . —-——— _- L. 1 +1 9 _ ._ I x—)>°O 4x3—3x2+2x—l Y y 4 A") 'k_ H3 ‘rlgéuj(x)J +C -_I L} —' 1“.“ ‘ L} - -_x,.: x 3%! m- ale); 4 i- c» a» ~~ L lef x =ln x+4+e’” ,then ’0 ,_ F, ' ("m 2 — 7 W )a, #3). 2 . f} 4 f 8. Usmgthesubstitgﬁon u=2x+1,fmd L\/2x+ldx. '(H .m- c .. J Jane #5 dot-«23W egg-Listed» , ,».r—- . : -i—,,r§.r_s,¢:..:‘>< .L a ._ {€353}? 3:139! ‘uti '“' t-- 3 2‘:\¢X"' _‘f I f. a -~:~ - 9 Ify=x2 Sinqx then ﬁnd 32 10. Let fbe the ﬁmc'ttonwﬁhdenvgtlve givenby Q . .. , 2 Hi 52X, 5m!” 4' K1 kz-Caﬂ/s) f‘(x)=x2 —-J—c~. Onwhatmtervalgsﬁs fdcc;easing? _' n ' ,, .. . / n P—Vji' , VI _ m:_ _ 0 {i reef/,7" ‘ \lJ’ZKOmg‘ ~K 'U/LX K4“ 5:: “0 la rte-3‘37» K * Dd“ 11. Let f be the function given by f (x) = 21:21. Find where the 1x2. A curve has slope 2x +3 at each point (x, y) on the curve. . — “ x - x1. . . . . . graph of Jj 15 concave dgyvn. g 10? ‘ i x '* X a)“ ’ 25 2" E Find an equatlon for this curve if it passes through the point WOOZ’Le My." ‘- 49' “iv (1.2). zit/5””? \1‘2“*"” K_ (:3? ’23:) {"2- 752} 2,3- +x ~33 13. Let f be the function deﬁned by f ( x) = 4x3 — 5x + 3 , Find 14. A particle :11 ves along the x~axis so that at time I 2 D it the equation of the line tangent to ﬁliegra‘ph of f atjthe point 9031mm is given by 3‘0) = 2t} ‘2”; + 72‘ _ 53 - At What where xzj1j(“f>1 alkali” ‘4’ '1" l7 {bf ' time tistheparticleatrest? ‘7 7: 7w 7 “3'4 a: 7x41! Wt): (951. Has +71 = cit”; 45 H1) 15. What is the slope of the line tangent to the curve _ ( 3y2 —2x2 26—2191 atthe point (3,2)? ' H —; A c: - 2- CW: Uu * H V NIL; 4x :th J h.) . U"; f, r, E ' r' ,1 " O.” ' ” .x A )4 j ’ ‘ '9' u a +:< M 2 - '1 t: . —---‘;—--~ an“- 3 V r f? | '3 2 ’1“ —, LnL lfz’y : 53w TX“ ‘JL_’1 44-97 7: q i f; 3r A. i", am L f '——_' — , 1(3) 2 a _. , ’ l“: U’H‘P t} + e + 61ft#—~ 71—7— A. TLJET f ‘\ These are also some of the problems that were in my AP Book as sampies. l picked out the ones that l thought’all of you should be able to do at this point (or at least have a good idea of where to Start.) They are also from the multiple choice section of the test (with a Calculator) but I did not give you choices (conservation of paper and I thought you could do them on your own). i picked 6 of the 17 in the section. The time limit for the 17 is 50 minutes with a CALCULATOR! Key points to remember: 1. The exact numerical value may not appear in a multiple choice answer so be ready to approximate the best numerical value (by rounding or truncating.) 2. Unless otherwise speciﬁed, the domain of a function f is assumed to be the set of all Real numbers x for which f (x) is a Real number. 3. The inverse of a trigonometric function f may be indicated using the inverse function notation f‘] or with the preﬁx “are” (e. g., sin"1 x = arcsinx ). 1. A particle moves along the x—axis so that at any time t 2 0 , its 2. The radius of a circle is increasing at a constant rate of 0.2 velocity is given by V“) 2 3 +4_lcos (Q90 _ What is the meters/second . What is the rate of increase in the area of the circle at the instant when the circumference of the circle is acceleration of the particle at time t = 4 ? (decimals) 20” metequ (exact in S of z ) 3. Let f be the ﬁmction with derivative given by 4. The velocity, in feet/second= of a particle moving aféng the x-axis is given by the function v(t) 2 e' +te' . What is the f ‘(x) = sin(x2 +1) . How many relative extrema does f have average velocin of the particle from time t = 0 to time t z 3 ‘2 ontheinterval 2<x <4? (decimals) 5. The function f has ﬁrst derivative given by 6_ Let g be the function given by g (x) : fsin (r2) dtfm, fr(x) = _....1G_3 I What is the wwordimte ofthe inﬂection —l S x 5 3 . Find the interval on which g is decreasing? . 1+x+x (decimals) ‘ any: "tat ( 'lz)( hr? pomt‘ofthe graph of f? (decimals) hi, I. B L” F V»: r ic-‘JJLIIEX i : y‘ I 3’2 in .1 a ‘— A"; U 2 IBWH :Wf) : 3 “in iCoS (0.9519) ¥HCEDi Li. ’("éiﬂiongf_)jﬁ (3-K? 'i‘“=;gi--").T laszZQ dr " *F7 “‘2 701‘. W3 ZBWZOZWLJ Ir :uv - Raﬁ z 33'? I.er c’r (Hf a i" i»;\ 5)\$'(><3:buiw in ‘t J i- l: r. 8 fine» 3 A x3 _, ,733 a”; _.. *‘aﬁewta‘r‘q’w ‘* ' I X: UQLWT " ...
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