It has nothing to do with x→ what, but it is related to the formula you use, such as x→∞, so ln( 1+x) has no corresponding Taylor formula, but if it is ln( 1+ 1/x), then Taylor formula can be used directly, because1/x →

In mathematics, Taylor formula is a formula that uses the information of a function at a certain point to describe the value near it. If the function is smooth enough, Taylor's formula can use these derivative values as coefficients to construct a polynomial to approximate the function value in the neighborhood of the point when the derivative values of the function are known.

Taylor formula also gives the deviation of this polynomial from the actual function value. Brook Taylor, an English mathematician,1one of the most outstanding representatives of the British Newton School in the early 8th century, was born in Edmonton, Oxfordshire, Delsey, England on August/865 1685.

170 1 year, Taylor entered St. John's College of Cambridge University. After 1709, he moved to London and obtained a bachelor's degree in law. 17 12 was elected as a member of the royal society. In the same year, he joined the committee urging Newton and Leibniz to debate the priority of inventing calculus. Received a doctorate in law two years later.

Since 17 14, he has served as the first secretary of the royal society, and 17 18 resigned on health grounds. 17 17 years, he solved the numerical equation by Taylor theorem. Finally, he died in London on February 29th, 173 1.

Due to work and health reasons, Taylor visited France many times and corresponded with French mathematician Montemor many times to discuss the problems of series and probability theory. 1708, 23-year-old Taylor got the solution of "vibration center problem", which attracted people's attention. In this work, he used Newton's instantaneous mark. From 17 14 to 17 19, Taylor was in the period of mathematical Newton.