Optimizing B for Inequality with Floor Function

MHB
Thread starter solakis1
Start date Nov 14, 2021

In summary, "solve for B given A for x > 0" means finding the value of variable B when variable A is known and the value of x is greater than 0 using algebraic equations and principles. The condition x > 0 is important because it limits the range of possible solutions for B. An example of solving for B given A for x > 0 is 3A = 6x + 12, where A = -8 and B = -6. Strategies for solving for B include using the distributive property and substitution. This phrase can also be applied to other types of equations, such as exponential or logarithmic equations, by using specific rules and properties.

Nov 14, 2021

solakis1

given $A>0$ find a $B>0$ such that:

For all $x>0$ and $x>B$ Then $|\frac{x}{x-\lfloor x^2\rfloor}|<A$
Do not use the concept of the limit

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Dec 5, 2021

solakis1

hint:[sp] $|\frac{x}{x-\lfloor x^2\rfloor}|$=$|\frac{1}{x}|.|\frac{1}{\frac{1}{x}-\frac{\lfloor x^2\rfloor}{x^2}}|$[/sp]

1. What is the formula for solving for B given A when x is greater than 0?

The formula for solving for B given A when x is greater than 0 is B = A/x.

2. Can this formula be used for any value of x?

Yes, this formula can be used for any value of x as long as it is greater than 0.

3. How do I know if I need to solve for B given A when x is greater than 0?

You would need to solve for B given A when you have a situation where you know the value of A and the value of x is greater than 0, and you need to find the value of B in order to solve a problem or equation.

4. Are there any restrictions for the values of A and x when using this formula?

The only restriction for the values of A and x is that x must be greater than 0. As long as this condition is met, the formula can be used for any value of A.

5. Can this formula be used in other scientific fields besides mathematics?

Yes, this formula can be used in other scientific fields such as physics, chemistry, and engineering where the concept of solving for one variable given another is applicable.