Determine the following limits at infinity.

l...

Question

Determine the following limits at infinity.

lim t→∞ (−12t^−5)

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. Find the limit of the given function at infinity. The limit as X approaches infinity of -35 multiplied by X to the power of negative. Awesome. So it appears for this particular problem we're asked to find the limit of this given function at infinity and we're provided a limit expression. So with that in mind, let's read off our multiple choice answers to see what our final answer might be. A is negative infinity, B is -1, C is 0, and D is 1. Awesome. So, first off, in order to find the limit of the function, which will write our function as F of X is equal to -35 multiplied by X to the power of -7. So we're trying to find the limit of this function as X approaches infinity, specifically positive infinity. We need to follow 4 simple steps, so we need to solve this problem in 4 easy steps. So our first step is we need to recognize that X to the power of -7 also means that it's equal to 1 divided by X to the power of 7. So, therefore, as a result, we could go ahead and write that F of X, so we could say that F of X. is equal to -35, and then we could take the negative 35 and we can multiply it by 1 divided by X to the power of 7. Fantastic. Awesome. So our next step is we need to recall and note that as X approaches infinity, we need to note that As a result, 1 divided by X to the power of 7 will approach 0. Because the denominator will become very large. So let's say that again. So as X as X approaches infinity, 1 divided by X to the power of 7 will approach 0 because the denominator, which I'll say capital D, becomes very large. So I just would, I drew an arrow pointing upwards. So the the denominator, which is capital D will become very large. That's what the upwards arrow means. So, our third step is, therefore we could go ahead, as we should recall, we should be able to write that F of X when we plug in our value for X into our expression, so we'll take that F of X is equal to negative. 35 multiplied by 0, because obviously 1 divided by 0 will give us 0, so that means that this whole expression will be equal to 0. So our last step is we could take the limit now. So the limit, uh, so the limit of F of X as X approaches infinity, so we could say that the limit as X approaches. So we can say that the limit as x approaches infinity of -35 multiplied by x to the power of -7 is equal to 0, and that's it. We found the limit. Hooray, we did it. And this means that X will approach infinity will be equal to 0, and this corresponds with multiple choice answer letter C. Which once again is 0. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Determine the following limits at infinity.

lim t→∞ (−12t^−5)

Key Concepts

Limits at Infinity

Negative Exponents

Behavior of Functions as t Approaches Infinity

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