Explain the meaning of lim x→a f(x) =∞.

Question

Accepted Answer

Welcome back, everyone. Which of the following statements describes the meaning of limit as X approaches K of G of X equals negative infinity? We're given 4 answer choices, let's analyze each of them. So first of all, we're given a, it says S X gets closer to K from the left, and this means that we can write limit as X approaches K from the left, which means that K must have a superscript with a negative sign, right, approaching K from the left. We don't have that, right? And then it says the values of G of X, so we are writing G of X, are negative in degrees without bound. So we can say yes, the limit would be negative infinity. Now in this case, A is not the correct answer because X approaches K and not K from the left. Now, let's consider B. It says S X gets closer to K but not necessarily equal to K. So this means that we're writing the limit as X approachesk without the left or right side, and then it says the values of G of X are negative and decrease without bound. So once again we add a negative sign and infinity because there's no bound. So B is the correct answer. Now let's analyze C. As X gets closer to K from the right, the values of G of X increase without bound. So here we have limit as x approachesk from the right. So we're writing a script with a positive sign because we're approaching K from the right. The values of G of X increase without bound, and this means that we now have positive infinity and not negative infinity. So there are two errors in this statement. We don't need a positive sign as a superscript to indicate the right side, and we should have negative infinity instead of the positive infinity. So C is incorrect, and this says S X gets closer to K but not necessarily equal to K. So this means that We are approaching K. The values of G of X increase without bounds, so we're taking G of X and in this case we get positive infinity because it says increase, right? So D is also incorrect. So the correct answer choice to this problem is indeed option B. Thank you for watching.

Explain the meaning of lim x→a f(x) =∞.

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