Coordination of aproximations in secondary school students’ understanding of limit concept

The aim of this research is to characterize the coordination of the processes of approximation related to the understanding of the limit of a function. We analyze the answers of 64 post-secondary school students to 7 problems considering the dynamic and metric conception of limit of a function. Results indicate that the metric understanding of the limit in terms of inequality supports that the student is capable of coordinating the approximations in the domain and in the range when lateral approximations coincide. However, the student is not capable of this coordination when lateral approximations do not coincide. This indicates that the metric understanding of the limit begins with the previous construction of the dynamic conception in case of coincidence of the lateral approximations in the range.

Cameron's proposals to limit EU citizens' access to the UK: lawful or not, under EU rules? CEPS Commentary, 29 November 2013

This Commentary briefly examines each of Prime Minister Cameron's headline proposals to limit EU citizens’ access to social benefits. Are these proposals in breach of the UK’s obligations under EU law? The paper also makes some general comments about the end of the transitional arrangements for Bulgarian and Romanian work-seekers, and ‘benefits tourism’ in general.

Uppermost Limit, Extent, and Fluctuations of the Timberline and Treeline Ecocline in the Swiss Central Alps during the past 11,500 Years

Pollen and macrofossils were analyzed at two sites above today's treeline (or tree limit) in the Swiss Central Alps (Gouillé Loéré, 2503 m a.s.l., and Lengi Egga, 2557 m a.s.l.) to test two contrasting hypotheses about the natural formation of timberline (the upper limit of closed forest) in the Alps. Our results revealed that Pinus cembra--Larix decidua forests near timberline were rather closed between 9000 and 2500 B.C. (9600-4000 ¹⁴C yr BP), when timberline fluctuations occurred within a belt 100-150 m above today's tree limit. The treeline ecocline above timberline was characterized by the mixed occurrence of tree, shrub, dwarf-shrub, and herbaceous species, but it did not encompass more than 100-150 altitudinal meters. The uppermost limit reached by timberline and treeline during the Holocene was ca. 2420 and 2530 m, respectively, i.e., about 120 to 180 m higher than today. Between 3500 and 2500 B.C. (4700-4000 ¹⁴C yr BP) timberline progressively sank by about 300 m, while treeline was lowered only ca. 100 m. This change led to an enlargement of the treeline-ecocline belt (by ca. 300 m) after 2500 B.C. (4000 ¹⁴C yr BP). Above the treeline ecocline, natural meadows dominated by dwarf shrubs (e.g., Salix herbacea) and herbaceous species (e.g., Helianthemum, Taraxacum, Potentialla, Leontodon t., Cerastium alpinum t., Cirsium spinosissimum, Silene exscapa t., and Saxifraga stellaris) have been present since at least 11,000 cal yr ago. In these meadows tree and tall shrub species (>0.5 m) never played a major role. These results support the conventional hypothesis of a narrow ecocline with rather sharp upper timberline and treeline boundaries and imply that today's treeless alpine communities in the Alps are close to a natural stage. Pollen (percentages and influx), stomata, and charcoal data may be useful for determining whether or not a site was treeless. Nevertheless, a reliable and detailed record of past local vegetation near and above timberline is best achieved through the inclusion of macrofossil analysis.

.08 BAC limit saves lives: why every state needs a .08 BAC law.

Mode of access: Internet.

Define and limit the jurisdiction of courts sitting in equity ... : report [to accompany H. R. 5315].

Submitted by Mr. La Guardia. Referred to the House calendar and ordered printed March 2, 1932.

Enforcement of the national maximum speed limit enforcement practices and procedures. Final technical report.

National Highway Traffic Safety Administration, Washington, D.C.