3943. Precise definitions for left- and right-sided limits Use the following definitions. Assume f exists for all x near a with x 7 a. We say the limit of f 1x2 as x approaches a from the right of a is L and write lim xSa+ f 1x2 = L, if for any e 7 0 there exists d 7 0 such that f 1x2 - L 6 e whenever 0 6 x - a 6 d. Assume f exists for all x near a with x 6 a. We say the limit of f 1x2 as x approaches a from the left of a is L and write lim xSaf 1x2 = L, if for any e 7 0 there exists d 7 0 such that f 1x2 - L 6 e whenever 0 6 a - x 6 d. Comparing definitions Why is the last inequality in the definition of lim xSa f 1x2 = L, namely, 0 6 _ x - a _ 6 d, replaced with 0 6 a - x 6 d in the definition of lim xSaf 1x2 = L?
April 13 , 2016 Medieval Art History: Study Guide – Exam #2 The exam will cover Chapter 4 “Early Medieval Art in the West” Exam Breakdown: 15 Multiplechoice questions (2 points each) 5 True/False questions (2 points each) 6 Short answer questions (5 points each) 6 Image identification questions (5 points each) – 3 pts. for title, 2 pts. for date Terms and Ideas: La Téne Celts – Northern European group, advanced metal workers, Mediterranean influence Fibulae – large safety pins for cloaks and other garments Polychrome or gem style – multicolored stones mounted in strips of gold, employed by the Goths to decorate jewelry, weapons and functional objects Huns – Attila = leader; from Asia Ostrogoths – Eastern Goths Visigoths – Western Goths Vandals – another outside force that sacked the city of Rome; Germanic Tribe King Luitprand – Ruler of the Langobards, patron of art and architecture Lombard – building technique High relief – more than ½ of the figure projects from the background Clovis I – Ruler of the Franks, adopted Christianity to ensure military victory Cloisonné – an ancient metal working technique, uses small metal filament and colorful glass enamel to create a luminous surface Viking – essentially a pirate, term generally applied to medieval Scandinavian culture Chipcarving – carving or fastening technique; derived from wood carving and designed to catch and reflect light Sutton Hoo – AngloSaxon burial cite, two cemeteries, buried in ships with their treasures, tent like element over it and burial mound over it Manuscript Illumination – religious texts, hand colored Carpet Page – a cross, geometric ornamentation and repeated animal forms Incipit Page – Introductory words or opening phrases in the text of a medieval manuscript Foederatii – indigenous allies Sacramentary – liturgical service book containing the priest’s part of the mass o Know the function of the images