Why is x equal to X when x in SiNx tends to zero

The proof of the theorem of rotunda in Calculus
Those who have not studied calculus can be proved in geometric sense
Let's draw a unit circle at the origin of the rectangular coordinate system, make a radius OA at the center of the unit circle, the included angle is x, and then make a vertical line through the X axis of a direction, intersecting with H
sinx =AH/R = AH
The arc length from a to (1,0) is equal to RX = X
When x is infinitely reduced, ah will gradually coincide with the arc and get x = SiNx

SiNx when x tends to zero, what is it equal to

sin0=0

Finding the differential of function y = e ^ xsin2x

To find the derivative of this function, we need to use the derivation rule of function product and compound function
y=e^xsin2x
y'=(e^x)'sin2x+e^x(sin2x)'
=e^xsin2x+e^xcos2x*(2x)'
=e^xsin2x+e^xcos2x*2
=e^x(sin2x+2cos2x).

Higher number: function expanded into power series
1. Expanding f (x) = 1 / x into a power series of x-3
2. The function f (x) = 1 / (x ^ 2 + 5x + 6) is expanded into a power series of X-2

1 f(x)=1/x=1/(3+x-3)=1/3*(1+(x-3)/3)=1/3 * ∑(n=0,∞)(-1)^n * (x-3)^n /3^n
2 F (x) = 1 / (x ^ 2 + 5x + 6) = 1 / (x + 2) (x + 3) = 1 / (x + 2) - 1 / (x + 3)

Seven times eight equals 56, 32 plus 56 equals 88. These two lines are written together

32+7×8=88

Given the power of X of function f (x) = 2, the power of absolute value of X of G (x) = 1 / 2 + 2. (1) find the range of function g (x). (2) find the power of X satisfying the equation f (x) - G (x) = 0
Why (1 / 2) ^|x ∈ (0,1],

Let u = | X|
Y = (1 / 2) ^ u is an exponential function and a decreasing function
u>=0
So y = (1 / 2) ^ u gets the maximum value at u = 0, which is 1
And always greater than 0
So it belongs to that range

The quotient of a number divided by its reciprocal is one thirty-six. This number is ()? Twelve tons is one-third more than (), and () tons is one-third less than twelve tons
When a number is divided by its reciprocal, the quotient is one thirty-six. This number is ()? Twelve tons is one-third more than (), () tons is one-third less than (), twelve tons is one-third less than (), and () tons is one-third more than twelve tons. Four to () equals twenty-five divided by () equals () to sixteen equals zero twenty-five, It is known that the price of trousers is three fifths of the top. How much is the price of trousers?

The number is (6)
12 tons, 1 / 3 more than (9)
(8) One third less than 12 tons
12 tons is one third less than (16) tons
(15) One third more than 12 tons
4 to (20) = 25 divided by (100) = (4): 16 = 0.25
240÷（1+3/5）x3/5=240x5/8x3/5=90
The price of pants is 90 yuan

Simplified formula
Title: (2 + 1) (2 square + 1) (24 power + 1) (28 power + 1) (216 power + 1) + 1
Ask to give the steps to solve the problem, each step had better be clearly written out, mathematical master speed to answer ah~~~~

Original formula = (2-1) (2 + 1) (2 ^ 2 + 1) (2 ^ 4 + 1) (2 ^ 8 + 1) (2 ^ 16 + 1) + 1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)+1
=(2^8-1)(2^8+1)(2^16+1)+1
=(2^16-1))(2^16+1)+1
=2^32-1+1
=2^32
Continuous square difference formula

Li Bai walked on the street with nothing to do. He picked up a pot and went to buy wine. When he met the shop, he doubled it. When he saw the flower, he drank a bucket (the bucket was an ancient vessel). When the shop and Hua finished drinking the wine in the pot, he asked how many buckets there were in the pot?

Suppose the original wine x Dou, he meets the shop three times and sees flowers three times at the same time. After the first meeting, the wine is 2x-1; after the second meeting, the wine is 2 (2x-1) - 1; after the third meeting, the wine is 2 [2 (2x-1) - 1] - 1 = 0; solving this equation, we get x = 78 (Dou). A: how much wine is there in the wine pot

One out of fifteen, five out of nine and five out of six

1/15、5/9、5/6
The least common multiple of denominator 15, 9 and 6 is 90
1/15=6/90 、5/9=50/90 、 5/6=75/90

Why is x equal to X when x in SiNx tends to zero