Hello,
This is actually not homework.
I was google searching for "proving trig identities from geometric point of view), found one of the result which proves trig identities using Euler formula. I really liked it. Easier, quicker & simple.
But when the author speak about sum to product formulas...
Thanks for quick reply. It is simple to start with R.H.S to L.H.S.
As per solution, they move from L.H.S to R.H.S, thats my question how to play with it?
Tried to get different common factors over and over, no success. It is supposed to move from L.H.S to R.H.S.
Hello,
While following problem solution found this $$ 4a^4 + 8 a^3 + 8 a^2 + 4a + 1 = ( 2a (a+1) + 1 )^2 $$
Trying to figure out how did author do it but failed.
Anyone?
Explanation is somehow terse. But problems are good. He divides them to exercises & problems. exercises are almost straightforward questions but problems make you think. In general, I would consider axler books between dry & rigorous levels. I took cohen as main book & axler as supplementary for...
Phase 1 (Gentle introduction) : Trigonometry by Lial. (Know concept in general without any in-depth explanation, easy problems to get used with subject + has good geometry refresher in first chapter).
Phase 2 (Better problem set) : Trigonometry chapters in precalculus by david cohen. Much better...
Hi,
Recently I studied triangle inequality and the proof using textbook precalculus by David Cohen.
My question is whats the benefit of this inequality ? One benefit I found is to solve inequality of the form |x+a| + |x+b| < c which make the solution much easier than taking cases. I assume this...
Hmmm. Good point! The issue here is that my point is "sometime true sometimes false" & your point "If it not true, then it is always false". huge difference between my point of view and yours! I believe it has something to do with "logical mathematics" if there is something called so.
The issue...
My answer is False! I think must stated "in general," in the beginning of the statement. Cause this could be true if f or g = zero. There may be other cases also.
Is my answer right?
Thanks.
Am not avoiding, am thinking in other ways. For this particular problem, surely x intersect with x^3 + 1 if draw both graphs. Clear intersection is there & I understood your point, but for this problem there is clear intersection.
Hello,
Am re-studying math & calculus aiming to start pure math studying later.
However, I got this problem in Stewart calculus.
Typically, this is a straightforward IVT application.
x = x^3 + 1, call f(x)= x^3 - x + 1 & apply IVT.
However I have two things to discuss. First thing is simple...
As I expected, this is not an easy question to ask & will go far.
Am really enjoying & appreciating these long replies even though I need to re-read it again & a little bit above my level.
Keep the discussion up gentlemen, one day I will have deep math knowledge & maybe I can join this discussion.
Thank you for your detailed reply. Surely, using calculus definition will clear any doubt.
Your way is gentle and great, but am looking for definition for the tangent itself without the idea of "approaching xo".
One idea came to mind, what about this "Tangent line is a line that touches the...