calc_review_3_2009_-_20100001

# calc_review_3_2009_-_20100001 - t i AP Calculus Name<6...

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Unformatted text preview: / t i '/ AP Calculus Name: <6 Review #3 Show a// work/M The fesf will be divided I'm‘a calculator and no calculator arfs. Evaluate each of the following (hint you can use shortcuts): . (3+h)4—81 . V81+h—9 _ 352—1 1. l1m01—h—~ 2. Llngw 3. . lmli 1 _; —-> x—> x_ 7. ﬁx) : 3x“ “F (074* ﬂue) = I)? ‘l‘O‘l: if; \$00: x “r“ *3: Q’V 108 ‘ 2 _ lim/ gtanx+1 5E l3 5 limcos(7r]:h)+1 'I 6.61'imt +t 2 4. 7% . h t 1 x—>—ﬂ x+ —->0 t—>1 _ 4 -Fév~7=-l:7'+/c I‘txlzlvkt’l " S \( ~ ‘ i ﬁx): law PM: Sec x ,5 “cl”? 1: mid-«9w \ ‘ a , ,1: W ):_ «so»; "' rowan =l ¥ (0‘74” * X ' ‘1 mt ' = » (0)451 :- Find the derivative of each function u 2—.shortcuts Be sure to use correct notation. 7. f(x)=(x2 +3)” Hm 2 39M» 3)“! 2x 10. y: (cscx+cotx)'l . 11. g(t)=sin(314) 3'12. y=(4x3+5)6 \l- -|(¢scx+co'lx)'z('05CXUJ-l'¥t’CSL/O 30%): C05 (“99%; 7‘; (a (4X3'l53§ l2 1 I l ‘Lééxw‘lxiwcx l a 9'53 608(3‘l3q \ L S ‘73.») 3‘” l l 7:7 X Wt” - l c m-ix)‘ " a W‘VV I 13. :5- :052 2(3x— 2) CS X 14. f(x)=‘/x_2_ 15 f(f)=sin3 (51d): (Sinlgf )> 4 1+x - o (549' D \{c gas (“'03 ﬁlm: l‘*"‘)"‘(t) 'xﬁimﬁl 790*) PM): 3(5mls/c cs ‘ _._____———————-Z——‘-"— : Y‘aQQOS (SK/19> (’ﬂnl'SX 1))(5) .U l+)u- > .[1 l : (HXUIL— \:‘A:' "L (1.2:)— __ l-tX-L —— 7K7— \ \7 \$ 1 (p L0\$<3 (page) (“4.6” — “+7334”: \C‘+¥L)1ll . Find an equation for the tangent line to the function at the indicated point. 11' 4 n (E7;l7"lt¢°l'g ’2‘“? y— +cotx—2cscx where x—E :3 344,0 ”10);; \$174» x {/7164 yup-ix {2(1), {sue} twrwlgpnbm m Find an equation for that tangent line and the normal line. to the function at the indicated point. 3 it)». wall 7“0); 9 i2; 18. DeTer_mine The poinT(s) aT which The graph of The funcTion has a horizonTal TangenT line. y=4x3—6x2—1 l yztwﬁ2wx2012x2ox42o I ' D c In (x—Qw _ \>< ' l 19 Given = x2 \l' WW>— 2’8" ”lx’w/él , XL' 2X ' y x1 /' IXﬂyb %«>> ”:33: a DeTermine The poinT(s) aT which The graph of The funcTion has a r'izonTal TangenT lI X 1’2’% :b ’/ “22,370 E) b. DeTer'mine The poinT(s) aT which The graph of The funcTion has a verTical TangenT line. @021) :0 20 Suppose f' (2): 4, g '(2)- — -3, f(2)- — —1, and 9(2): 2 Find The derivaTive aT 2 of The following a. s(x)= f(x)+5g(x) 5 ‘(X): g. (X) + 5310(3 5‘03: l—l 1k SC—g) : 'll 9‘60: 4 (ﬂ ~3‘CX)+ 500 HEW} f(x) 9‘0— : "l . (23) -\— a . U4) : E g(x) (230A): 503-? 0‘3 2 {3(5) glad: 2(4) - (—I) 23) S d. h(x)=f(g<x» ma)- 10 ‘ (goo) 9‘“) , {‘(Tu) 5:05 2§W L’l '5: "7' f0?) ,k(x)= f(g(x)). Fill in The missing enTr‘ies in The Table using The g(x)' h2‘M WW) + 5m Poe) informaTion abouT f and 9 given in The Table and The definiTions of h ,j, and k _-—__l_— EINIIIIIIKIIIHIIIEIIHHIIIEII IIMIHIIIIIIIIIIIIIIIIIIIIIII IIIIIﬂIIIIIIIIIIIIIIIIiﬂIIIII b- P(><) = f(><)9(X) q(x)- — 21. LeTh(x)= f(x)g(><). J'CX)= Use your calculaTor' To differenTiaTe each funcTion aT The given value of x, r‘ound To 3 decimal places. 22. y=cotx2,x=12r- » 23. y=Vx2—5,x=10 ' l I . — ,‘I/lo .7:~8.O®ILI I“) 24. Find The average raTe of change for The funcTion over The iven inTerval. .mn= 2+ww mmi 9g . -+CT) ia> , @RTwoSTa-(2+u60> AX' Tno Ti 25. Some values of a funcTion f are given in The Table below. TI _ --lII-- X “El-”mu \hur Kali? Winkle 0. Use This Table To esTimaTe e value of f'(2) In Three differenT ways. - . ~c, "la Tog Log: 3Illo'l 7‘0‘36‘7 ~33 ”2.4:? ’Iwgﬁvwog,‘ "3“ —308 J '1 . 0 / 37' ’ ~ ——"S. a,IA1 3 9©>-1 ‘ 204437 3 b. Judging from The values in This Table, do you Think ThaT f(x) is differenTiable aT x : 4? JusTify your answer. q ’- g I q g g 1 9- ’q r a 7 )0 4+ _ 3. 4 0' I “l- 0 I’ Ll 26. The graph of a funcTion f is given below. EsTimaTe The values of f'(x) aT The following poinTs using TangenT lines. a.x:-2 b.x=—1 c.x=1 d.x=2 ...
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