Section 1 of 1Question 4 of 7Marks for thisUpload answer sheetsEvaluate: $ dz where € is given by ze2 -2iz Iz/ =...

After reading this section, write out the answers to these questions. Use complete sentences. What is the approximate value of $r^{n}$ when $n$ is large and $|r|<1 ?$

In this question. Here we record the entirety, revert you off the expert, and again you go to the expert and less one over and less one. Plus, the constancy in this question were given a definite integral from 12 to 3, minus three off X square T x. First we can bring the monastery outside and would write. The fraction is the exponential form Pirmin Institute, The X. Now we applying this formula here, get a man Street hams. This one will bless one to the power. So have the experiments. One hour, minus one from 1 to 2. Yeah, the Manus Manus cancel out. So we should get one over X and then three outside here from 1 to 2. And then we look in the limit now. So getting close to the 3/2, uh, minus one. Number one ministry over one will be three here. And then we get ICO, too. Here we have two. And then minus, uh, this one will be managed three out of two. And that's gonna be the answer

Evaluate this given integral here. And in order to do that first have to keep in mind is that it's a good thing they told us that if is differentiable so then continue to use U substitution. We're going to set U equal to half of three x plus one. Therefore do you is equal to have prime of three X plus one Time saturated the inside which is times three X. So now we need to get out of Prime three Express one index by itself because that is what we have in the numerator. So we're going to divide both sides by three. So we'll have 1.3 Do you sequel to have Prime three x plus one TX from here? We have integral off one over you. Do you times one third. That means we've got 1/3 Allen of you plus C. That further becomes 1/3 of hell enough. USF- three x swan plus see that's her full evaluation right there.

The stock about question 83. So, in this case, after valued presently good, let's take the trio because the constants will be out of one one minus. In fact, let's take the four outside from the economic. So when we take the four outside, we have one more four over here and just become r minus one looks but square for a student. Let's take back Well say so. Three is already in the new monitors that we have three over to here and the girl off dear. Over one deer were squared off one of our four minus R minus one. This further simplifies to three or two. Integral off, dear. Over this candidate on us one or two squared minus R minus one square squared. Recall a formula Darty X over square off a square minus six square. Integral assigning waas. Excellent. In this case, excess replaced by R minus one at any one word. So around so becomes 3/2 time signing was X, which is R minus one and K, which is one of work. That's the concert over bigger, etc. The final answer himself. That's three or complaints and it was the scruples and drop you have want minus Don't that's some constant of C

In this question here, Where you calling about the definite integral. So if we have the f come toe ranks as the equal to f prime here in Cochin FX, then we will have integral from me to be on the function F X t X equal to the captain on the B minus F come to on the A C minus here. Now in this question were given the integral off the two X minus 3/4 T X from 0 to 1. Now, the first time we need to find anti derivative on the function inside. Now untie the river them the two x obviously equity, the X square anti derivatives 3/4 equals 3/4 X. Now we evaluate this one and the zero and one, and then we took an equal to hear it will be the one square ministry of a far one times one of the miners, the zero square minus 3/4 times zero. Then we get equal to one minus three under fall. Then we get equal to the one off the fall on This will be the answer