Prove that | SiNx | is less than or equal to | X| Classified discussion, using derivative method.

Prove that | SiNx | is less than or equal to | X| Classified discussion, using derivative method.

Let y = | sinx| - | x|, then this function is an even function, symmetrical about the Y axis; Let's first discuss the right side of the y-axis: y = sinx-x, derivative: y ˊ= Cosx-1 "0, then y ˊ It is a decreasing function, so SiNx is less than x, so | SiNx | is less than or equal to | x |. If you don't understand, you can continue to ask

How to find the differential of y = (SiNx) ^ 2?

y=(sinx)^2
y'=2sinx(sinx)'
y'=2sinxcosx
y'=sin2x

The zero point of function f (x) = - x + X + 1 on (1.2) is

x=1.32471795724475

Square of high school factorization X - 5x + 6= My formula is (X-6) (x + 1), but the answer is (x-3) (X-2). Of course, the answer is right. Ask a master to give the process

x ²- 5x+6
=x ²- 2x-3x+6
=x(x-2)-3(x-2)
=(x-2)(x-3)
Cross multiplication:
1 -2
1 -3
x ²- 5x+6=(x-2)(x-3)

Square + (a + 1 / a) x + 1 factorization of X RT...

Multiply with cross
x^2+(a+1/a)x+1=(x+a)(x+1/a)

Use factorization to calculate: (1-5 square parts) (1-6 square parts) (1-7 square parts). (1-200 square parts)

Square difference
=(1-1/5)(1+1/5)(1-1/6)(1+1/6)(1-17)(1+1/7)……(1-1/200)(1+1/200)
=(4/5)(6/5)(5/6)(7/6)(6/7)(8/7)……(199/200)(201/200)
Middle divisor
=(4/5)(201/200)
=201/250