make-the-given-changes-in-the-indicated-examples-of-this-section-and-then-solve-the-resulting-pr-414

Question

Make the given changes in the indicated examples of this section and then solve the resulting problems.
In Example $3,$ change $n$ from 10 to 5 .

Oswaldo Jiménez · Accepted Answer

we will approximate the value of the interval from 2 to 3 of x times square root of x plus one. By the trap aside the rule With five serve intervals. So first let&#x27;s define the function F of x equals X times square root of X plus one which is the integral. And we define that function on the closed interval 23. And with that we calculate now the step size age which is the common distance between any two consecutive notes And is the length of the interval of integration 3 -2 over the numbers of intervals here considered which is five And this gives us 1/5, That is 0.2. With that we now determine the notes we get to use and these are it&#x27;s not equal two ex want equal 22 X two equal 2.4 X three equal 2.6 X four equal 2.8 And X five is the last note equal three. These are the knows we&#x27;ve got to use and with this we can say that the interval from 2 to 3 of x times squared of X plus one Is approximately equal to T5. That is a trap. So the rule with five serve intervals which is the finest age. Half times the image of the first note. X note plus two times the image of the second note plus two times the image of the third note, Last two times the image of the 4th note Plus two times the image of the fifth note and plus the image of the last note which is X five. Remember here is X four. Just put it correctly. Okay so this is a formula of trump&#x27;s of the rule with five of intervals. And this give us equal to Ages 0.2 That over two times F at two last two F At 2.2 Plus two f. at 2 4 Plus to have a 2.6 plus To have a 2.8 Plus F. at three. And is equal to 0.1 times. The image attending note is next time squared of X plus one. So it&#x27;s for F for X equal to yet To score 2 3 plus. Uh We have this factor to out and The image is 2.2 square root of 2.2 plus one. So it&#x27;s two times 2.2 will be 4.4 squared off 3.2 plus two times. Sorry, just put the result. These two times 2.4 is 4.8 Squared off, 3.4. Last two times 2.6. It&#x27;s 5.2 squared off. Okay, that&#x27;s pretty. You do better. 52 square it off. Uh 2.6 plus one is three 0.6 plus. Then we have two times 2.8. 5.6 Squared off. two plus 1 is 3.8 plus three sq- four. That is we can But the result here is 2 3 times to six. Okay, so you have this now uh in this moment we gotta use a calculator. And we have used that. We have you used a calculator and we found that disease. Uh This is opportunity equal to four point 69685 3954 084 95 seven. It is the integral from 2 to 3 of X times square root of X plus one separate, ultimately equal to four point 69685 395 for 084 957, which was calculated using traps. So the rule with five sub intervals and this Approximations of the interval, you&#x27;ve got to be less accurate than that found in example three. Because there uh We use tens of intervals, but here we are using less of intervals. We&#x27;re using 5 76.

Lourence Gonhovi · Answer

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Lourence Gonhovi · Answer

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Jason Taylor-Pestell · Answer

I really like how this book talks about you. Substitution. It&#x27;s a really helpful way Toe understands these more complicated questions because one way to approach this is you distribute the square, you distribute the to distribute the square. I mean, you would factor, but this factor times itself and then yeah, distribute. Um, but then you&#x27;re then you&#x27;d have to simplify combining like terms and then factor that. But there&#x27;s actually a much simpler way here. This looks like a try. No meal. If I let you equal five and plus one, then really, what I see here is you squared plus two times you minus three equals zero. And this is an incredibly easy try. No, be able to factor. We have a coefficient of one on the use where term The only things that multiplies. A three or one in three. And we need to get a two from subtractions. So that means that says it&#x27;s positive the three has to be positive that what has to be negative. And then from here we can use the zero product property U plus three house equals zero. Or you might this one house single zero subtract three from both sides on this equation. Add one to both sides on this equation. U is equal to negative three or you is able to What now? This does not solve the problem because all we&#x27;ve sold for as you now we&#x27;re going to substitute five M plus one into the equation and used that to solve for in much of the original variable. That&#x27;s right. It&#x27;s one. All right, so subtract one from both sides. Here&#x27;s have dropped one from both sides here. This is five and equals two. No divide both sides by five. This one is five and equals zero. Divide both sides by five, and we end up with and is equal to 2/5 or zero. Is that the two solutions that should work? If I substitute zero in, then I&#x27;ll have one squared plus two times one minus three, and that equals zero. So that checks out. That&#x27;s also to fits in five times. 2/5 is 10 deaths, which is to +13 squared nine 2/5 times five again is two plus one is three, three times to his six. That doesn&#x27;t look like it&#x27;s going to work. Minus three equals zero That&#x27;s not true. All right, so I&#x27;m gonna post the video to figure out what happens, and I will be right back. All right. Sorry about that. Um, So I made a mistake in this piece right here. I put the three enough thinning to three. So this should actually be negative three minus one So that instead of two, this is negative for hopefully you found my mistake before I did. This is negative. 4/5. Right? So I&#x27;m gonna change my solution here. This is one of the reasons why it&#x27;s so helpful to substitute back in and check your solution. Because it&#x27;s quite possible you might make a mistake like I did. And we want to be able to identify those mistakes. And since one of them worked, that&#x27;s what let me know that the other one definitely like the process was good, but I made a mistake in copying, which is a very common mistake. Um, so now let&#x27;s substitute again. If you substitute negative 4/5 in here, you know, negative 25th which is negative for plus one is negative. Three squared is still nine, but then here is gonna be negative three times to which is negative. Six. And that&#x27;s what I was expecting to get. So this is negative six and the negative threes that does equal zero. So this checks out. We&#x27;ve We&#x27;ve found my mistake and these are the two solutions and is negative 4/5 Brenda zero

Kerry Thornton-Genova · Answer

we are solving for n. Let&#x27;s begin by subtracting three m from both sides. Three Him minus three m is zero. Thus, we have a minus 3 a.m. on the left equals negative two times Ben on the right, nor to get rid of the negative to we must divide both sides by negative to negative to buy by Negative two is one and one times end is just n Thus we end up with a minus three m divided by a negative two equals and

Cory Kuzinski · Answer

3/5 n 3/5 of some number is equal to negative three tents. All right, so when we&#x27;re when we&#x27;ve got a variable being multiplied by a fraction and we want to get that variable by itself, the easiest way is actually to multiply by the reciprocal of that fraction, because then they end up with 15 over 15 times in 15 15. Send is one end, or you might look at his three over three is 15 over five is one, so we just end up with N So if we multiply by 5/3 on the left, we also have toe multiply by 5/3 on the right. I always like to try and simplify before I multiply. So I&#x27;m looking at like negative three over three is like negative one over one and five over 10 is like one over two. And then we can multiply numerator times. Numerator negative. One times one is negative. One denominator times denominator. Two times one is two. So our answer is negative. 1/2 3/5 of negative. 1/2 is negative. Three tents. Let&#x27;s check that and make sure it&#x27;s true. So we&#x27;re gonna take 3/5 times and which we know to be negative. 1/2 or we think is negative. 1/2. We&#x27;re gonna see if that equals negative. Three tents you see pretty quickly. It does three times negative. One is negative. 35 times two is 10. So negative. 3/10 equals negative. Three tents. That means our answer negative 1/2 is the correct answer.

Problem

(a) approximate the value of each of the given in…

Problem 2 Easy Difficulty

Make the given changes in the indicated examples of this section and then solve the resulting problems.
In Example $3,$ change $n$ from 10 to 5 .

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Anna Marie V.

Kristen K.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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Basic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Grace H.

Anna Marie V.

Kristen K.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus