What is the definition of function limit when x → x0?

What is the definition of function limit when x → x0?


Let f (x) be defined in a neighborhood of point x0. If there is a constant a, for any given positive number ε (no matter how small it is), there always exists a positive number δ, such that when x satisfies the inequality 0



Whether the necessary and sufficient condition for the existence of the limit of a function at x0 requires that the left and right limit values are equal to f (x0)


Our team will answer for you~
For example, f (x) = x, when x is not 0, f (0) = 1, and the limit of F (x) at 0 is 0
Both left and right limits are equal to f (x0), which is a necessary and sufficient condition for f (x) to be continuous at x0



If the volume of a cube is known to be 10 cm3, the surface area of the cube is () cm3
I don't have a calculator with a root,


a=10^(1/3)=2.15443,
a^2=4.64159,
S=6*a^2≈27.85cm^2,
The surface area of the cube is about (27.85) cm ^ 2



Xiaohong uses three small cubes with a surface area of 12 square centimeters to form a cuboid. What is the surface area of this cuboid?


36-4-4 = 28 cm2



In January, the average outdoor temperature is - 5 C from January 1 to 8, - 7 C from September 9 to 21, and - 9 C from January 22 to 31


(-5*8-7*13-9*10)/31
=(-40-91-90)/31
=-221/31
=-7.129 ° C



In January, the average outdoor temperature is - 5 ℃ from the first to the eighth, 7 ℃ from the ninth to the 21st, and - 9 from the 22nd to the 21st. What is the average temperature in January


=[-5*8+(-7)*13+(-9)*10]/31= -221/31= -7.1℃



In the middle of January, the outdoor average temperature is - 12 ℃ from January 1 to 8, - 12.5 ℃ from September 21, and - 12.9 ℃ from September 22 to 31. What is the average temperature in that month?
The question is practical


It is known that the average outdoor temperature from January to August is - 12 degrees, so the total temperature of the 8 days is - 12 * 8 = - 96 degrees, and the average temperature of the 13 days is - 12.5 * 13 = - 162.5 degrees, and the average temperature of the 22-31 days is - 12.9 degrees, so the average temperature of the 8 days is - 12.9 * 10 = - 129 degrees, so the average temperature of the 31 days is



In January, the outdoor average temperature from the 1st to the 8th is - 5C, from the 9th to the 21st is - 7C, and from the 22nd to the 31st is - 9C, then the average temperature of the area in January (with two decimal places) is a good bonus


(5*8+7*13+9*10)/31=7.13
The average temperature is about 7.13



In January, the average outdoor temperature is - 12 ℃ from the 1st to the 8th, - 12.5 ℃ from the 9th to the 21st, and - 12.9 ℃ from the 22nd to the 31st?


[8X(-12)+13X(-12.5)+10X(-12.9)]/31
=[-96-162.5-129]/31
=-387.5/31
=-12.5 (℃)



What do big three, small three and pure five mean?
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