The graph of ℎ in the figure has vertical asymptotes at x=−2 a...

Question

The graph of ℎ in the figure has vertical asymptotes at x=−2 and x=3. Analyze the following limits.

lim x→−2 h(x)

Accepted Answer

Welcome back, everyone. In this problem, we want to analyze the limit of G of X as X approaches -3 using the graph of G as shown. The dashed lines represent the vertical asymptotes at X equals -3 and X equals 2. A says it's infinity, B negative infinity, C 0, and D says it's 2. No What can we use from our graph to tell us what the limit of G of X would be as X approaches -3? Well, we can start to look at the limit of our function as it approaches -3 from the left and the right side. And if both of those limits are the same, then that can tell us what the limit is as X approaches -3, OK? So in other words, If The limit Of X approaches -3 from the left of G of X. OK. Is equal to the limit as X approaches 3 from the right of G of X and let's say both of those equals some limit L. Then That means the limit of G of X as X approaches -3 is also going to be equal to our L. Now, what is that limit going to be? Well, on our graph, notice that at our line X equals -3 for our function approaching from the left, G of X is going to grow arbitrarily large as X approaches -3, OK? So, from the left. The limit of G of X as X approaches -3. Is going to be equal to infinity. Likewise, if we look at the limit from the right hand side, notice that G also increases arbitrarily, OK? In other words, the right hand limit. Is also equal to infinity. Since both of them are equal to infinity, this tells us then that the limit as x approaches -3. Of geopics is also going to be equal to infinity. Therefore, A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

The graph of ℎ in the figure has vertical asymptotes at x=−2 and x=3. Analyze the following limits. <IMAGE>
lim x→−2 h(x)

Key Concepts

Vertical Asymptotes

Limits

One-Sided Limits

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