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# CALCULUS I MATH 141

GPA 3.51

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This 5 page Study Guide was uploaded by Cassidy Grimes on Monday October 26, 2015. The Study Guide belongs to MATH 141 at University of South Carolina - Columbia taught by Staff in Fall. Since its upload, it has received 48 views. For similar materials see /class/229545/math-141-university-of-south-carolina-columbia in Mathematics (M) at University of South Carolina - Columbia.

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Date Created: 10/26/15

Study Guide Thanksgiving 2003 Hope everyone has a pleasant Thanksgiving weekend This homework as signment will get you off on the right foot for studying for the nal exam This will be due on December 1 Write each problem up so you can 1150 your work as a review sheet for the rest of the week before the nal exams Our exam will be held on December 8 at 900 in our same meeting places Show all work Work should be written in an orderly manner with simple descriptions of what expressions or equations mean so anyone can understand the logical ow of your arguments Simplify into Sines and cosines tan3a sec4z csc5c cot6r r 3 I A I Cu 6 Les 7 9 If 573915 7 my Evaluate limkgto sin4r csc8m I l L M 5394 0 EX quotI quot sin10 a 2 XM Wm 4XL Xquot 4 sw Evaluate limb tan4 cot52 539 and MSW 4 7 In quot Liyi L I39VI f f 1 90 I inf 5 5 we ML aw 9h sin z 6zs Evaluate kink 24 1 v q xix 3 HM nx zx l xiv Hm Small 7L g gt F L M MW 3739 Evaluate hm 1 L w M 239 xvl x IX X 4 w k Y as Evaluate limp 32312 4H1 quot39 L L Z 39 L 5 3gt 9 Evaluate 11mmgt00 azifgitt 1 L L 7 HM x16 M M V 1 V I 3 O L gt M 3 Xgt5a Yv f sv 7 3 343 49 1 Evaluate lunmaoo if l quotl V t L w w m i 1 r gt yaw x r 3X quot1 7 33 YAquot l Is the function y 5 23 wellde ned at 1 0 Why is it important to know if the limit Hm 5 23 exist or does not exist N sl we Bvl39 lf the l lwfrl Wart wt kn def w LJ 1 71 4 v0 s a mum ls Mt Wu wle A mew ws Jr What are the three basic types of discontinuities that we have studied Give an example of each type 959m w3 4 V lchw196 Is the function f continuous at x07 at x 1 7 Explain why or why not Explanation should involve a limit Nat LmL t iwwul not 2950 A 3 M 010 9f 1mk quot4 0 L I W HMMS En Vlr HM i L h w L Hr 7 xt Vl Is the absolute value function a continuous function at x0 39 at x 6 7 Explain why or Why not Explanation should involve a limit Tu Jhwk MIL Mkhm is Lmvmwi wuhwiwc Tu M M 1 9 0r throw el H271MS m We 139 I Lquot 7 4 Lm i iwopw yams w mu Using the de nition of the derivative what is the derivative of 2 with respect to x 1 x 1cm x M m am 7 im w om i 1 F f 39 k i f k n n K Using the de nition of the derivative what is the derivative of i with respect 19 i i m Hm i Lu W t h a we mu h 5 Using the de nition of the derivative explain why the absolute value function does not have a derivative at i 07 M Q B M L j i2 XgtMtf 5 l l y C at k K m AMnthtC ai Ii Ii Mt i i i t List the SIX trigonometric functions and their derivatives mart m S 514 ac gt Losy yc 1 7 Lqi 7 09 7L KU Ms y 4 aw 5 v SE v a 7L n rm SacLi a e c 3L 3 What are the derivatives with respect to a of the following trigonometric functions sin3r cos5x tan71 and csc8w 54 3 Des t im5 74 fiez fr 43c R L 3 What are the second derivatives with respect to t of the following trigoni metric functions Simit tos15t and tan9t s H Nth fe 7 L quot M bay igt t gt drymls l 7 17399 at E 14 9 g a sum 72iga e7 it 7 quotv 515876 0 quotIt 7 A H j i 5 What are the antiderivatives with respect to f of the following trigonometric functions sinlt c0505 and sec291 l gt L 14 C L v M m C j i Evaluate i c053tzm34 OAK P39VW 3 x 3 01M qqxi ma lwl3 q L m4 lx Evaluate if sin17c 3 Prwk 14 311 013 3 14Ls 5l4 7 l 4 3 Evaluate gun re I VCvkL 3X MHkzl H x cilz7x 3 w sn l i x x Find a if 1y 7 Izyz sinfxy 81 93M Simlhw io k w 3 4 3 339 C31t 11 11 5491 w 1 g FindifV m 3ifrisafuuction oft w Lw quotHy 4 dLd IL rzdE 1 cu df d X Findifv1rr2h lfr audhare functions oft by AL 94 JUquotLV3914 LUA E rl ldr 3LTrrz k r f dm H At 4 q M dt 439 A 39Iquot UL IV If a baseball is thrown straight up in the air at 96 feet per second how high will it go How long will it stay in the air t 3 L V 1t ua gt 42 t ib 1 5 IH mt Mw quotM mt My in NM WW 5 1 1cl7 r ib Wu 5w fut e76quot f 39l l39 W 6 law a va If a baseball is dropped from a 480 feet tall building how fast is it going aw Aa t1 80 a when it hits the ground u 771 fie Z I 21 V14 um K ZJI LH s W l 1 50 V3i WW m n Find the smallest value of the function y 4x g m c7 W A 139 fw new 7quot 4 2 v05 3 1 LN Find the dimensions of the largest rectangle that can t in the region bounded by the parabola y 12 7 12 and y 0 Am pf wow 1K 3 1y l1 x1 ZKxl CM XCLt tvi qul wt 3 AM gt AA Manu L WW 10 dl Q m r of r 7 6130 6531Y kL 1 Y 1 27 2 3 LenkaQ m outw ww L4 WWW 7 74 that ck

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