1, sinx = x-1/6x3+o (x 3), these are sine expansions of Taylor formula, and sinx can be replaced by Taylor formula expansion when seeking the limit.
2. Arcsinx = x+1/6x3+o (x 3), which is the arcsine expansion of Taylor's formula. Arcsinx can be replaced by Taylor formula expansion when seeking the limit.
3.tanx = x+ 1/3x 3+O (x 3), which is the tangent expansion of Taylor's formula. Tanx can be replaced by Taylor formula expansion when seeking the limit.
4.arctanx = x- 1/3x 3+O (x 3), which is the arctangent expansion of Taylor formula. When seeking the limit, we can use Taylor formula expansion instead of Arctanx.
5. ln (1+x) = x-1/2x2+o (x2), which is the expansion of Taylor's formula. When seeking the limit, ln( 1+x) can be replaced by Taylor formula expansion.
6. Cosx =1-1/2x2+O (x2), which is the cosine expansion of Taylor's formula. When calculating the limit, Taylor formula expansion can be used instead of Cosx.
Brief introduction of Taylor formula:
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 solved the numerical equation with Taylor theorem, and finally 173 1 died in London on February 29th.
Taylor is famous for the theorem that functions are expanded into infinite series in calculus. This theorem can be roughly described as follows: the value of a function in the neighborhood of a point can be expressed by an infinite series composed of the value of the function at that point and the derivative values of each order. However, for half a century, mathematicians did not realize the great value of Taylor's theorem, which was later discovered by Lagrange. He characterized this theorem as the basic theorem of calculus.