I

x ∈ ⟨-2, 0⟩ right?

|ℝ|=𝖈=+∞ So its better use x∈ℝ

But how did you get the -25 and 26 to execute your Grouping Technique? I first found that 5 is a root of the polynomial, then executed long division with x-5, then found that resulting 2nd-degree quotient had no solution, thereby leaving 5 as the only root.

x <= -2 NOT x >= -2

I mean why not just square it

Oops. Proofread.

Thanks ❤❤❤❤

your words and diagram are correct but the writing is wrong. it should read x<=-2

10q so much

Didn't the properties of absolute value inequalities say u < -k or u > k then you would also get the correct x <= -2 or x >= 0

I personnaly don't like the way you do it. I think you should treat 3 cases : 1.when x<-5 2.when -5<x<3/2 3.when x>3/2 even tho it is longer to do, there's also no risk to have a wrong answer at the end

Happy Holidays to you.

I’m very excited for this as I was not a fan of Trig in high school. I started school again recently for Comp Sci and am falling in love with Math all over again.

Thank you so much for such a wonderful exercise. :) needs more puzzles like this to make mind used to of the visual decodation of Functions and its respective Derivative. Will be awesome if it will go to higher order derivative too.

|u|=|w| ⟹ ±u=±w

Where is trigonometry Playlist?

I see people talking about checking their answers. Let me explain my course of action as someone who will be taking calculus 3 in a couple weeks (assuming i pass the final) Checking the answer can be a pain. However, sometimes you take, not the best path for getting the answer and end up with numerous extraneous solutions and only 1 real answer. As someone who personally has seen this. I always check my answer. Then i double and triple check those checks. I used to never check my answer... and somehow this worked all the way up until calculus 1. I dont know how. I guess i got lucky. When calculus 1 hit logarthims kicked my butt. You cannot take the log of a negative number. Yeah, check your answers. I did not. However, i also learned checking your answer takes time. So i learned through some very good professors, you do not always have to check your answers. For example, a simple quadratic, or solving a simple log might need a check, but you can do a "lazy check" which involves just checking if its in the domain. Overall: checking your solution is necessary, and i tend to look for 3 things: if im doing the absoulute value. If im doing a log. And most important, if im doing the integral. I triple check these.

I was doing it in my head and I almost forgot about the second solution lol

Thanks for a very IMP pointing of crossverifying solution by putting back to equation. I will make sure to keep that in mind hereforth !

Ah, yes...the bane of my students' existence: checking their solutions. I'm glad this one didn't have any extraneous solutions, but the number of students who forget to verify their answers for absolute value equalities and inequalities will always amaze me.

There should be 4 roots as we can write it as x+5 = -3 +2x.

actually pretty darn cool, thanks for sharing

dy/dx

Note: In the final answer, the absolute value on the natural log could be omitted since (1+4y^2) is always positive.

The answer is the sqrt 2

Don't forget +C

😢

Harharmahadev

(*´∇｀*)(*´∇｀*)(*´∇｀*)

Very beautiful sweet tq ❤❤❤

😊0p😊😊😊😊0

😂

😡😡😡😡😡😡

M🌄 0:52 🪹

राहुल गाँधी महारथी है जब राहुल गाँधी से पीछे धक्का लगा बीजेपी सांसद आई सीओ पहुँच गया अगर आगे से धक्का लगा होता तो भगवान् के प्यारे हो जाता

😊😊😅😊😅

Soul of Mozu Romeo

Now do product rule with full factored form 😂 Not the power rule or any other rule 😂😂

I don't know why we have to do that rearrangement, I can see it working even without that step: p¹¹-64p⁸-p³+64 p⁸(p³-64)-(p³-64) (p⁸-1)(p³-64) ... It still gives the same result even without that rearrangement. Why do we have to rearrange, though?

(a+b)²=a²+2ab+b²

The answer is (pie/8+1/4)

I love this stuff. It’s in my DNA after 60 years. After doing so many problems you don’t need the tables anymore. I just love to see these examples worked out again. THX. Keep them coming.

Hmm.. that seems to be useful for differential equations. Thank you. :)

👌👌

I am not at calculus yet but if this is what it's like then needless to say, I'm terrified

Or you could just do a u sub with u=(t/2) was easier imo

Still can’t believe I passed calculus two with a C.

On m=-2 just the square root of a number is always positive, so m≠-2 and m=7

Voice break “factor out the foURr”