Hey there, math nerds! Today we're going to talk about limits. This is some seriously cool stuff, so buckle up and get ready to learn!
First Limit Example
Now, this is a pretty tricky limit example. But don't worry, we'll break it down together. The key to solving limits is to approach the given value from both sides. We'll start with the left side.
As x approaches 0 from the left, we can see that the function is approaching -∞. Now let's check the right side.
As x approaches 0 from the right, we can see that the function is approaching ∞. Therefore, this limit does not exist.
Second Limit Example
Okay, now let's take a look at this beauty. This is a prime example of the squeeze theorem. The squeeze theorem states that if you have two functions that are both approaching the same value, and a third function that is always between them, then the limit of the third function must also approach the same value.
So, as x approaches 0, we can see that both the sin(x)/x and x/cos(x) functions are approaching 1. And since |sin(x)/x| is always less than or equal to 1, we can use the squeeze theorem to determine that the limit of sin(x)/x must also be 1.
There you have it, folks! Limits can be a bit intimidating, but with a little practice and some sweet tricks like the ones we discussed today, you'll be a limit-solving machine in no time. Keep on crunching those numbers!
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