How is lim x🠂0 sin x/x used in this section?

Question

Accepted Answer

Welcome back, everyone. In this problem, we want to determine the limit as X approaches 0 of sin 17 X divided by X, using the fact that the limit as X approaches 0 of sin X divided by X equals 1. A says the answer is 1, B 1 17th, C 17, and D says the limit does not exist. Now, how is this limit, how is this fact supposed to help us figure out the limit as X approaches 0 of sin 17 X divided by X? Well, let's think about what this limit is saying here. Basically, all it's telling us is that the limit as X approaches 0 of a sine function divided by its argument will be equal to 1. So in this case, if we can make the denominator of our given function equal to the argument of the sign, then we can apply this fact to help us solve. So let's take the limit, OK, as X approaches 0 of the sign of 17 X divided by X. How can we make our denominator X? Well, we could multiply our denominator by 17, but if we do that, we'll also have to multiply our numerator by that constant 17. So now, we could rewrite this as the limit as X approaches 0 of 17 multiplied by the sign of 17 X divided by 17 X. Now if we take this a step further, we can take our constant outside of the limit, so that 17 multiplied by the limit as X approaches 0 of the sine of 17 X divided by 17 X. No, the sign of the sign of our function, or sorry, the sign of the argument is being divided by its own argument. OK. The argument here is 17 X and it's being divided by 17 X. so we can apply that fact, OK, to then say that this entire expression is going to be equal to 1. So that's 17 multiplied by 1, which equals 17. Thus, the limit as X approaches 0 of 17 X divided by X equals 17. C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

How is lim x🠂0 sin x/x used in this section?

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