Usually in the study of limit problems, will encounter more complex problems, in this paper, we discuss how to use the concept of equivalent infinitesimal better limit operation. At the same time, in the process of research, we re-explore the proof of Taylor's formula, and find that some functions have a similar expansion form to Taylor's formula, that is, 'fractional expansion'. It is also found that after the linear combination of Taylor expansion and fractional expansion, the obtained expansion is more accurate, which helps us to have a better understanding of the approximation of function expansion.

The regularity and variability of the composition distribution of the pyrolysis products of corn stover fermentation residue and phenolic resin with the pyrolysis temperature were investigated by thermogravimetry (TG) and lyser-gas/mass spectrometer (Py-GC/MS). The results show that toluene, phenol and methyl phenol are the main common components of the two systems, 2,3-dihydrobenzofuran, alkoxy compounds and a small amount of carboxylic acid are the unique components in the pyrolysis products of corn straw fermentation residue, while dimethyl phenol, 9H-xanthene and other components in the phenolic. This is a reflection of the differences in the composition and structure of the two raw materials.

Lianghuai Mining Area is one of the 13 large coal bases in China. It is an important coal and coal production base in China. Mine water inrush accidents occur frequently, resulting in economic and human resource losses, reflecting the importance of the study of hydrogeology in mining areas. In this paper, the hydrogeological conditions of Bozhou and Huainan Panxie mine are analyzed, and the similarities and differences between the hydrogeological conditions of the two mines are summarized. The shallow pore water group in the Bozhou area is composed of the Quaternary system of the Quaternary system (Q4d) and the upper part of the upper part of the Mao Tong group (Q3m). The lithology of the aquifer is silt, silt and fine sand. The shallow pore water group of the Panxian Pancho Formation in Huainan is composed of the Upper Pleistocene of the Quaternary system and the Holocene strata. The lithology is mainly composed of fine sand. The main sources of shallow pore water supply in the two areas are precipitation infiltration, mainly for evaporation, lateral runoff, artificial mining and deep flow and discharge to the river.

With the development of material life, the importance of plants in life has become increasingly prominent, and indoor flowers are also popular. As we all know, plants have purified air, refreshing brainwashing, promote sleep, sterilization and other effects, such as mint, Clivia, aloe and so on. Therefore, the choice of plants corresponding to their own needs is particularly important, while to note that some flowers should not be placed indoors. And different flowers on the water, temperature, light, soil and other requirements are not the same.