1. If -1/infinity = infinity or -infinity ?
2. If lim x->infinity^- = infinity & lim x->inifinity^+ = -infinity, then lim x->infinity = does not exist. Am i right? If im wrong please tell me the reason why?
1. To determine the value of -1/infinity, we can use the concept of limits. In this case, as the denominator approaches infinity, the fraction approaches zero. So, -1 divided by a very large number (infinity) is approximately equal to zero. Therefore, the value of -1/infinity is zero.
2. You are correct. If the limit of a function as x approaches infinity from the left (denoted as lim x->infinity^-) is infinity, and the limit as x approaches infinity from the right (denoted as lim x->infinity^+) is -infinity, then it can be concluded that the overall limit does not exist.
The reason for this is that the function does not approach a single finite value as x goes to infinity. Instead, it diverges towards positive or negative infinity depending on the direction from which you approach infinity.
Therefore, if the left and right limits at infinity have different signs (one positive and the other negative), or they approach different values (not including infinity), the overall limit does not exist.