There are two ways to find the limit of infinity: if there is a denominator, divide it first and then calculate it; If there is no denominator, create a denominator and then calculate the total score. Generally speaking, the method of creating denominator is inversion. Inverted substitution is a mathematical problem-solving method. Through the variable substitution of x= 1/t, the original mathematical problem with x as the independent variable becomes a mathematical problem with t as the independent variable, thus reducing the difficulty of the problem or simplifying the problem-solving process.
Extended data:
1 and ∞ are symbols representing infinity.
Aristotle (384-322 BC), an ancient Greek philosopher, believed that infinity could exist, because finite quantities were infinitely separable, but infinity could not be achieved.
/kloc-in the 20th century, a great Indian mathematician, Bascara, appeared, and his concept was close to that of theory.
The symbol of putting 8 horizontally as ∞ to represent infinity was first used in john wallis's paper Arithmetic Infinity (published in 1655).
2. See if two infinitely simplified symbols are different. If so, the result can only be ∞.
3. If the symbols are not different, see if the structures of the two infinitesimals are similar after simplification. For example, is infinity reduced equal to subtraction plus a non-zero constant? If so, the result is this constant.
4. If the signs are not different and do not belong to the second case, then the result can only be 0 or ∞.
Assuming that both of them are positive infinity, in this case, the monotonicity of logarithmic function can be used to perform logarithmic operation on the two terms of the original formula, because the 0 or ∞ obtained after logarithmic operation is exactly equal to the result of the original formula (monotone function satisfies one-to-one mapping).
After logarithm, the original formula is transformed into log(∞/∞), and the real part can be simplified by L'H?pital's law.
5. It should be noted that when ∞/∞=0, the original result is-∞. Although the logarithm is meaningless at this time, the same result can be obtained according to logx→-∞ when x→0+ (forward approaching 0).