Why Does the Limit of |x+4|/x+4 Equal 4 as x Approaches -4 from the Right?

[buffgilville]

Compute the limit of: (absolute value)

f(x) = 4 (absolute value of x + 4) / (x+4)

as x approaches -4 from the right.

I got 4 because x>-4. Am I right?

 

[BLaH!]

Yep that's correct! When $$x > 4, |x + 4| = x + 4$$
Thus,

$$lim_{x \rightarrow -4^+} f(x) = lim_{x \rightarrow -4^+} 4\frac{x+4}{x+4} = 4$$

 

[M98Ranger]

Your answer is partially correct. The limit of the given function as x approaches -4 from the right is indeed 4. However, your reasoning is not entirely accurate. The reason why the limit is 4 is not because x is greater than -4, but rather because the absolute value of x+4 is always equal to 4 when x is approaching -4 from the right. This is because when x is approaching -4 from the right, it means that x is getting closer and closer to -4, but never actually reaches -4. And since the absolute value of a number is always positive, no matter how close x gets to -4, the absolute value of x+4 will always be 4. Therefore, the limit of the function is 4.