b> A > 0 proof B-A / b

b> A > 0 proof B-A / b

The left and right are both (B-A) / b. is the middle one (LNB) / A or ln (B / a)

When a > b > 0, then 0 ＜ 1 / a ＜ 1 / b Can prove the properties of eight inequalities,

a>b>0
a> 0, b > 0, so AB > 0
So divided by ab at the same time, the unequal sign remains the same direction
So a / AB > b / AB > 0 / ab
1/b>1/a>0
I.e. 0 < 1 / a < 1 / b

A proof of mathematical inequality, known - C / a < - D / B, BC > ad. proof: ab > 0

-C / a ＜ - D / B is
c/a>d/b,
Multiply AB on both sides to obtain:
bc>ad,
The inequality sign does not change direction
Description AB > 0
It can also be proved by counter - evidence
If ab ≤ 0
Then we know that C / a > D / b
Multiply AB on both sides to obtain:
bc≤ad
This is contrary to the known BC > ad
So: ab > 0

[senior one mathematics] proof of relevant inequalities: known a > b, ab = 1, proof: a ²+ b ² ≥2√2 （a-b） It is known that a > b, ab = 1, verification: a ²+ b ² ≥2√2 （a-b）

(a ²+ b ²)/ (a-b)
=[(a-b) ²+ 2ab]/(a-b)
=(a-b)+[2/(a-b)]≥2√2
‡ minimum value of the original formula = 2 √ 2

Help prove two mathematical inequalities, 1. A ^ 2 + B ^ 2 + 5 > = 2 (2a-b) 2. A ^ 2 + B ^ 2 + C ^ 2 > = AB + BC + ca

Shift a ²+ b ²+ 5-4a+2b≥0（a ²- 4a+4）+（b ²+ 1+2b）≥0（a-2） ²+ （b+1） ² ≥ 0, so a ≥ 2, B ≥ - 1. A ²+ b ²+ c ²- ab-bc-ca≥02a ²+ 2b ²+ 2c ²- 2ab-2bc-2ca≥0（a-b） ²...

Help me calculate calculus Integral (y ^ 2) * [e ^ (- x * y ^ 2)] dy Offline x online x ^ 2

((-1/(4x))-x/2)e^(-x^5)+(1/(4x)+1/2e^(-x^3)
Idea: using step-by-step integral method;
Split (y ^ 2) * [e ^ (- x * y ^ 2)] into: Y / (- 2x) and (- 2x) Ye ^ (- XY ^ 2)
The integral is the integral of Y (Dy), so x can be regarded as a constant
Finally solve