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How to judge the infinity of multivariate composite function
The existence of no limit can be proved by the pinch theorem.

If the pinch theorem can't be proved, try to use Robida's law in the molecular formula to see the highest degree of the denominator. When all the positive formulas in the numerator denominator are added up, you can directly look at the highest degree. If both tend to 0, then the denominator is high and the limit does not exist. If both tend to infinity, then the molecular degree is high and the limit does not exist. Construct channels, for example, let y=mx or y = the square of MX.

Multivariate compound function refers to binary and above, which contains many unknown functions. In addition, in mathematics, the derivative method of multivariate composite function mainly adopts chain derivative method. When chain derivatives are used, one variable is derived, and the other variables are regarded as constants. If the partial derivative of multivariate composite function is required, the key of the method is to find a good path, and the chain rule is a good solution tool, and its formula can be simply written as "line multiplication, line addition"