Let me rewrite what I just wrote. G of x squared. Home Questions Tags Users Unanswered. I’m assuming you had paused the video and you had attempted to do this. I know we wanted the first five terms of this thing, but bear with me. Let me say it in a less confusing way. Sign up using Facebook.
Sign up or log in Sign up using Google. Video transcript – [Voiceover] Let’s see if we can find the Maclaurin series representation of f of x, where f of x is equal to x to the third times cosine of x squared. We’ll see how this thing right over here is going to be useful. But when you realize that, “Hey, gee, “if I can just re-express this function “as, essentially, “x to a power times “something that I know the Maclaurin series of, “especially You kind of see where this is going. That will give me another polynomial, another power series, and then I multiply it time A x to the n, and that’s going to, once again, give me another power series, and that will be the power series for my original function.
Let mxclaurin just use a new color. But when you realize that, “Hey, gee, “if I can just re-express this function “as, essentially, “x to a power times “something that I know the Maclaurin series of, “especially Well, we know how this, what this is like. If I wanted to write it as, I guess you could say as a function, or if I want to construct it using g of x, I could rewrite it as x to the third times We’ll see how this thing right over here is going to be useful.
As I know I have to calculate the first, the second, the third deriavtive of the initial function, but how does it work in this case? The second derivative, this is going to be painful. When you actually see what we got, you realize it would have taken you forever to do this by, I guess you could say, by brute force, because you would have had to find the 19th cosx of all of this madness.
But it’s only going to get more and more painful as we take the second and third and fourth derivative.
How do you find the maclaurin series expansion of #f(x)=cos3x#?
And I’m just rereading it for you, this is x to the third times g of x squared. Sign up using Facebook. If you’re seeing this message, it means we’re having trouble loading external resources on our website.
Then you’re going to multiply that times x to the third. Video transcript – [Voiceover] Let’s see if we can find the Maclaurin series representation of seriez of x, where f of x is equal to x to the third times cosine of x squared.
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So x to the third times g, g of x squared. Function as a geometric series.
Let me get myself some space right over here. You could just do this. I encourage you to maclakrin the video again and see if you can work through this.
Maclaurin series of sin x. But we just care about the first five terms, the non-zero terms, and we’re just saying this is an approximation, anyway. That actually will be the Maclaurin series representation cos3xx what we started off with.
Post as a guest Name. There are the Maclaurin series approximation of that is going to be one minus x squared over two factorial, plus x to the fourth over four factorial, minus x to the sixth over six factorial, plus, and I could keep going on and on and on.
mclaurin Visualizing Taylor series approximations. Then the third and fourth derivatives are going to be even more painful.
We say g of x is equal to cosine of x. G of x is just cosine. We’ve done that in the previous video.
Taylor Series of cos(3x^2)
But we already know from that, and this is one of the most famous Maclaurin series, we know that this is a g of x. In this case, I have to find the Maclaurin series, which is: Zauberkerl Zauberkerl 1, 1 7 I will give you a hint.
We actually will get the Maclaurin series representation of this thing right over here. If it’s equal to some A x to the n power, times some coss3x If you want to see that again, there’s another video.