This is exactly the same misunderstanding you had before.Please help me?
I think i understand: √x² = |x| Because the square of x when square-rooted could be negative or positive. (Is my understanding correct?)
I do not understand: |x| = -x
This is exactly the same misunderstanding you had before.
If \(\displaystyle \large x<0\) then \(\displaystyle \large |x|=-x\).
Now as \(\displaystyle x\to -\infty\) it is the case that \(\displaystyle x<0\).
While that is true , it has nothing to do with what was asked.On the other hand, if the limit was approaching positive infinity, it would be the case that X>0, so you would have put X instead of -X. It is a case-by-case situation.
Yes, if x>0 then |x| = x.
Yes, it is a case by case situation. Just look at the definition of |x|. Sometimes |x|=x and other times |x| = -x. So which definition do you use? Well it depends of the value of x. For example |-4| = -(-4) = 4 while |14| = 14
√x² = |x| since when you put in a positive number it comes out positive and if you plug in a negative you get back a positive number just like the absolute value function.View attachment 11776
Please help me?
I think i understand: √x² = |x| Because the square of x when square-rooted could be negative or positive. (Is my understanding correct?)
I do not understand: |x| = -x
bbm25, this is my last try at helping you see this. You may need a live tutor to guide you step-by-step.Also, why do i have to convert √x² into |x| and only then divide each value by the highest power in the denominator as shown in the example above? Why can't i just take the denominator's highest power (which would be just √x²) and divide everything straight away without converting to absolute value first? What happens if i do not?
My standard answer to "what happens if I do something other than what you teach?" is, try it and see!Also, why do i have to convert √x² into |x| and only then divide each value by the highest power in the denominator as shown in the example above? Why can't i just take the denominator's highest power (which would be just √x²) and divide everything straight away without converting to absolute value first? What happens if i do not?
Also, why do i have to convert √x² into |x| and only then divide each value by the highest power in the denominator as shown in the example above? Why can't i just take the denominator's highest power (which would be just √x²) and divide everything straight away without converting to absolute value first? What happens if i do not?
Fair question with a simple answer. While |x| sometimes equals x and other times equal -x it is the case that x ALWAYS equals x. So no need to replace x with -x (because they are NOT equal to one another)Why doesn't the x in the denominator (x + 1) also become -x?
This was in response towards the book! The picture i took, not towards what you've been teaching me! Apologies!!!