How to find limit at Infinity | Basics and Examples | Hindi/Urdu скачать в хорошем качестве

How to find limit at Infinity | Basics and Examples | Hindi/Urdu

Infinity is a very special idea. We know we can't reach it, but we can still try to work out the value of functions that have infinity in them.In the previous section we saw limits that were infinity and it’s now time to take a look at limits at infinity. By limits at infinity we mean one of the following two limits. In other words, we are going to be looking at what happens to a function if we let get very large in either the positive or negative sense. Also, as we’ll soon see, these limits may also have infinity as a value. First, let’s note that the set of Facts from the Infinite Limit section also hold if we replace . The proof of this is nearly identical to the proof of the original set of facts with only minor modifications to handle the change in the limit and so is left to you. We won’t need these facts much over the next couple of sections but they will be required on occasion. In fact, many of the limits that we’re going to be looking at we will need the following two facts. The first part of this fact should make sense if you think about it. Because we are requiring we know that will stay in the denominator. Next as we increase then x will also increase. So, we have a constant divided by an increasingly large number and so the result will be increasingly small. Or, in the limit we will get zero. The second part is nearly identical except we need to worry about being defined for negative. This condition is here to avoid cases such as. If this were allowed we’d be taking the square root of negative numbers which would be complex and we want to avoid that at this level.Note as well that the sign of c will not affect the answer. Regardless of the sign of c we’ll still have a constant divided by a very large number which will result in a very small number and the larger x get the smaller the fraction gets. The sign of c will affect which direction the fraction approaches zero (i.e. from the positive or negative side) but it still approaches zero. 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