m-repeat-exercise-37-for-the-functions-mathbfft3-sin-t-4-sin-3-t-mathbfgt1-8-sin-2-t8-sin-4-t-mathbf

Question

[M] Repeat Exercise 37 for the functions
$\mathbf{f}(t)=3 \sin t-4 \sin ^{3} t$
$\mathbf{g}(t)=1-8 \sin ^{2} t+8 \sin ^{4} t$
$\mathbf{h}(t)=5 \sin t-20 \sin ^{3} t+16 \sin ^{5} t$
in the vector space $\operatorname{Span}\left\{1, \sin t, \sin ^{2} t, \ldots, \sin ^{5} t\right\}$

Mike Gaerlan · Accepted Answer

in order to find our double prime unalterable crime. First, we need to find our prime of tea. So to find our priority would just do component lies. Differentiation. So derivative of co sign is negative signs. We&#x27;re gonna have negative three because of chain role a three science three t and then comma derivative Sinus cosigned. So we&#x27;re gonna have for co sign of 14 1,000,000 comma And then again, derivative of consign his negative science will have, um negative six sign six t now we confined our double prime, our double prime here. So we&#x27;re going to, um, it&#x27;s bye bye. Three again and then derivative coz I or Sinus cosigned, then here. Derivative coziness. Negative science. We&#x27;re gonna have a negative 16 sign for tea. And then lastly, we&#x27;re going to have a negative 36. Ah, design of six t here. So that&#x27;s gonna be our double prime a t. Next. In order to find our triple Prime a T, we&#x27;re going to take the derivative of that. So here, derivative of co sign is negative sign. So we&#x27;re going to have a positive 27 sign of three t here, then four times 16 is negative 60 or 64 on derivative of science Because science is gonna be negative. They&#x27;re negative. 64 co sign of four t and then lastly, six times 36. That is gonna be 216. And derivative clothes line is negative. Sign. We&#x27;re gonna have negative 216. Sign of six t. So this is going to be our our triple prime here. Sorry. This should be a positive since drew it of, Ah, co sign is negative sign, okay?

Chris Trentman · Answer

were given a vector function were asked to find its derivative. The vector function is R T equals 80 coastline three t i plus B sine Cuba T J Plus seized co sign cute T k The component functions of our which are 80 co sign Cuba t The sign Cuban T and sees Cho sang keep t are all differential And so it follows that our is differential in that are prime of tea is by definition the vector whose components are the derivatives of the component functions of our So we have our prime of t is equal to eight times co sign of three T minus three a t sign of three t I plus three b signed square tee times co sign T J plus minus three c co sine squared tee times Sigh Inti So we&#x27;ve been negative. Outfront It&#x27;s negative. Scientist E Okay, this is our answer.

Darshan Maheshwari · Answer

question on what 21 in this case were given immigration as is equal before we treat by I&#x27;m signed Treaty Buzz four or five by names Crossfire fee. So we have to find a veritable so very But they will be the differentiation off s with respect to be DS or didn&#x27;t even be This is a constant So this comes up, say, and the better great sign treaty. Then again, this is a constant So for five Break himself said and then we differentiate cost 50 So for what rebating means editors over here we have to use The change is so different station of Sinus cause we have caused treaty and then we defend ship Train these different station off three D Villagers to be three like ways we go over here, the transition off course is minus same minus and 50 and different station off. Five days is just five against change. So this streak, it can sell this by gets cancer. So what are we left with? Let&#x27;s take this four over by oh, safe. So if we take it outside the elephant forward bribe bracket caused three D minus saying for your feet. So this is the final answer. Divided your B s over

Adrian Fan · Answer

if this problem were calculating a derivative using the channel so we&#x27;re giving s is equal to four over street high quantity. Sign forward through time. Sign of three T plus four or five pie times. Co. Sign off quality five t. So we&#x27;re going to cut clay D s over DT so you can calculate the derivative of the first part here first. So it&#x27;s going to be over three pie. That&#x27;s a constant. Then we know that the revenge of the sine function is co sign. So we have co sign of three T, but he also after Adam and multiplied by another factor. That&#x27;s the derivative of the Inter Function three, which is three tea with respect to T. That&#x27;s just contribute, agree, and then we&#x27;ll do a similar thing here. We have to take for five high and then the derivative of the coastline function is negative. Sign to get negative sign of tea, but we also have to multiply by the derivative of the inter function. That&#x27;s five tea with respect to T. So that would have to multiply by five shares. Well, so we have a little bit of cancellation. The three here, the three here. Cancel out for the five here on the five. Here. Cancel out. So the final answer after a little bit of factory going to be forward high on the quantity co sign of three t by this sign of five T.

Doruk Isik · Answer

in this problem. We&#x27;re giving this system and then we&#x27;re us to test the system for the new year. So you gracious, you want Temple? Let&#x27;s see. To tempt Poseidon T plus C three times co Sense guarantee waas c seven times come sign six. Empty then should be zero. And the only system that satisfies the separation should be the trivial solution. So policies should be zero. So we could thing to do B 0123 or fire six. So we&#x27;re different values of be it. This equation should still hold, since Ulysses should be zero. So let&#x27;s form a system. Let&#x27;s form a system of before a C is zero. You are A matrix would look like this. He would have one here and then co sign of zero. Who&#x27;s on spirit of zero votes in Cuba? Zero at the dot Co sign 600 on second row be without one the sun consignment. And so the first rise 40 0 Enough! 41 up. 36 Go sign one goes I have Scrabble one votes and you go on co sign states one And you were that one Go sign too. Co sign six hour, too, and blasted. You would have won Ho signed six and coastline six. Power sits. Now, let&#x27;s go like this system you could use. I use meth that we could use meth up or any Elin troll to wait this values. So we were down 111111 one. And here we have 111 old wasn&#x27;t first role. And here we have 0.95 We have 0.99 and the last element is pulling 316 Now, if you sold for this system knowing your corruption metrics looks like this, uh, first of all, mentions a is convertible, so it means that you can actually find a solution. And if you sold this using math, lab or intellectual, you see that the only way to satisfy this is if all the seas are zeros. So since this is the oldest solutions, as trivial solution is the only solution. We&#x27;re going to say that this set is linearly independent as only the trivial solution

Problem 38 Easy Difficulty

[M] Repeat Exercise 37 for the functions
$\mathbf{f}(t)=3 \sin t-4 \sin ^{3} t$
$\mathbf{g}(t)=1-8 \sin ^{2} t+8 \sin ^{4} t$
$\mathbf{h}(t)=5 \sin t-20 \sin ^{3} t+16 \sin ^{5} t$
in the vector space $\operatorname{Span}\left\{1, \sin t, \sin ^{2} t, \ldots, \sin ^{5} t\right\}$

Answer

Observed that most of the function values of the function $1+\mathbf{h}(t)-\sin (5 t)$ are moving very
closed to the $y=1$ line. Therefore, our conjecture is verified.

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Anna Marie V.

Kayleah T.

Samuel H.

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Vectors Intro

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Observed that most of the function values of the function $1+\mathbf{h}(t)-\sin (5 t)$ are moving veryclosed to the $y=1$ line. Therefore, our conjecture is verified.

Linear Algebra and Its Applications

Anna Marie V.

Kayleah T.

Samuel H.

Joseph L.

Vectors Intro

Vector Basics - Example 1

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Anna Marie V.

Kayleah T.

Samuel H.

Joseph L.

Observed that most of the function values of the function $1+\mathbf{h}(t)-\sin (5 t)$ are moving very
closed to the $y=1$ line. Therefore, our conjecture is verified.

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications