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Midterm Study Guide: Mastering Calculus Concepts and Techniques

School
Connecticut College**We aren't endorsed by this school
Course
MAT 112
Subject
Mathematics
Date
Dec 11, 2024
Pages
20
Uploaded by AmbassadorSummer14910
(V@FSIO/\ , 3 - | (KEW MAT 112 MIDTERM Sign the honor pledge. Show all work. “Box up” final answer. " Good luck! VT
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(/o@;% ‘H:UX%—S 54X = find y® Use logarithmic differentiatio orporatin glg rithmic properties, to fdth derivative. )7 (j (* *‘5> [fm/\{] /ng /n (X*‘Ssg(’\ foy = 0 (xa S §a60) 4n = Qfl (X+3) + 4, fin&\ yrrza Doeivectives .. 167[71 Z /"fiA‘f 4 / | :"—"Z'( ><1‘5'>+ S‘/wx(&x> ( \ . C'OJK — = + = Y Ej = 20X+ Sia % ( - - C = U\z 5 \‘ - w‘} ZX"\‘(O- - O—E S(J, L ;yfl:"’w‘ N = mflfl X[ELT(O T @Jr%];
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<> P 4 2 5 4oot ladder is leaning aéainst a house when its ba‘s,e starts to slide away. By the time the base is 23/ feet from the house, the base is moving at the rate of 7 feet per second. At what rate is the angle between the ladder and the ground changing then?
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70 , 7C ( : ; Z) = 2 (18 PF<) - Z Use the “definition of the derivative” to find the derivative of the given function. (Write ALL the appropriate notation in the appropriate location of EVERY line, showing EVERY step. Don’t write any notation when it is no longer appropriate).
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N2 in \/Tmeoemn//#w’cisml i~ ‘6. Derivatives of the inverse trigonometric functions d{sin™" ) 1 du ul bt e - e O T, dx V1 — 2 dx g (.’(COS—J lfl . B 1 di dx - V1 — ,2 dx’ ditan”' w) 1 g dx 1 u? dx d(f—‘_‘z{__l_ ) . | du dx 1+ ,2dx d(seci 7 B i ~ du dx - lulVu? - 1 a&’ d(cse™ u) R i du 7 i - ;2 dlx lul Vu? —
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