Estimate the following limits using graphs or tables.

Question

$\lim_{h \to 0} \frac{\ln (1 + h)}{h}$

Accepted Answer

Hello there today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem, determine the given limit with the help of a table or graph. The limit of X approaches zero of the natural log of one plus five X divided by five multiplied by X. OK. So it appears that we're trying to take the specific limit and we're trying to figure out what its value of the limit is. And that is our final answer that we're ultimately trying to solve for. Awesome. So once again, we're focusing on the limit as X approaches zero of the natural log of one plus five X divided by five X or five multiplied by X. OK. So with that in mind, now that we know that we're trying to evaluate this limit, let's read off our multiple choice sensors to see what our final answer might be. A is one, B is two C is zero and D is DNE which means does not exist. OK. So first off to better help us, you know answer this problem or to help us solve for this problem, let us plug in our limit into our graphing calculator or whatever graphing software we're familiar with and comfortable with using. And when we do that, we will receive the following graph when we plug that into our graphing software or graphing calculator. And as you could see, I always call these L graphs because it's shaped like an L. And as we can see, we have it go, it follows the vertical axe very closely. The Y axis is the vertically axe and it crosses the vertical axis at about, it looks like one it appears. And let's make, let's indicate that in blue because our graph is drawn in red. So the blue dot that I just put on the vertical axe is at 0.01. Awesome. So that's when our graph intersects with the axe. And then it appears it follows the horizontal X axe very closely, but it does not cross the X axis from what we can see from our graph. So with that in mind, as we should recall a note, in order to estimate the limit as X approaches zero, we need to look at the graph for the function of F of X is equal to the natural log of one plus five X divided by five X. So once again to repeat, so in order to estimate the limit as X approaches zero, we can look at the graph of the function F of X equals the natural log of one plus five X divided by five X. So as we should note, as X approaches zero from the left side, which I'll use a capital L to denote left, that will mean that F of X will approach one in this case. So as X approaches zero from the left hand side, F of X will approach one. And similarly, as X approaches zero from the right side, F of X will approach one as well. So that means our final answer without a doubt has to be number one and that's it we've solved for this problem. Hooray. So looking at our multiple choice answers, the correct answer has to be the letter A which once again is one. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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Estimate the following limits using graphs or tables.
$\lim_{h \to 0} \frac{\ln (1 + h)}{h}$