- #1
singedang2
- 26
- 0
[tex]\lim_{x\rightarrow\infty}\frac{\sin|x|}{x}[/tex]
[tex]\lim_{x\rightarrow 0}\frac{|x|-|x-2|}{x-1}[/tex]
thanks!
[tex]\lim_{x\rightarrow 0}\frac{|x|-|x-2|}{x-1}[/tex]
thanks!
Last edited:
The absolute value of a number is the distance of that number from zero on a number line. It is always a positive value.
Absolute value can impact the behavior of limits, as it removes the negative sign from a number. This means that when taking the limit of a function involving absolute value, we must consider both the positive and negative values of the input.
The limit at a specific point for a function involving absolute value may not exist, as the function may approach different values from the left and right sides of the point. In this case, the limit would be undefined.
To solve a limit involving absolute value algebraically, we can split the function into two separate pieces, one for the positive values and one for the negative values. Then, we can take the limit of each piece separately and combine the results to find the overall limit.
Yes, limits involving absolute value can be graphically represented. The graph may have a "corner" or "pointed" shape at the point where the absolute value function switches from positive to negative or vice versa. This can help us visualize the different behaviors of the function from the left and right sides of the point.