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Problem 70 Easy Difficulty

Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.

$ y = 1 - x + e^{1 + x/3} $

Answer

see graph

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Video Transcript

So for this problem, we're going to ask graph the equation. We want to find the equation of the slant. Assam tope. So first, we're going to have y equals one minus e. I want my ex, That is plus e the one plus X over three. Okay. Okay, then once we do this, we see that we have our excellent ask them to right here. Now they're saying ask them to It's gonna have a negative slope. So we'll have something like Why equals negative x onda? That appears to be a potential state Assam tote. However, it's possible that we could, um, at one and get it even closer. So you see, if we do this, then our graph gets as close as possible without ever actually reaching it. That would be our state Assam tote. Why equals negative X plus one And again that was found by looking at this graph realizing that there is a slight Assam two right here and then ultimately we can kind of just gauge what the value is by plugging in different numbers. Also, we recognize that it needs to be a negative slope because it's going this direction. We also see that we can get it closer and closer to the value by increasing the Y intercept