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Aug
26
comment Don't see the point of the Fundamental Theorem of Calculus.
And why did you suddenly turn the $\approx$ into $=$ ?
Aug
26
comment Don't see the point of the Fundamental Theorem of Calculus.
ie: Did you imply this step? $$\frac{A(x+h)-A(x)}{h}\approx f(x)$$ $$\lim_{h\to 0} \frac{A(x+h)-A(x)}{h} \approx \lim_{h\to 0} f(x)$$ $$\lim_{h\to 0} \frac{A(x+h)-A(x)}{h} \approx f(x)$$ $$A'(x) \approx \lim_{h\to 0} f(x)$$
Aug
26
comment Don't see the point of the Fundamental Theorem of Calculus.
In the following, why are you able to say A'(x) = f(x)? I missed the connection. Did you take the limit of both sides in the section prior? $$\lim_{h\to 0} \frac{A(x+h)-A(x)}{h} = A'(x) = f(x)$$
Aug
26
comment Don't see the point of the Fundamental Theorem of Calculus.
This made the point the most clearly. The integral is actually defined independently of the derivative. The integral is merely defined the anti-derivative, but it is the Reimann sum of rectangles under the curve. Later on, one that can attempt to tie them together as "inverses using the FTC.
Aug
3
revised Exchange Rate scenario. Which is the better option?
added 271 characters in body
Aug
3
comment Exchange Rate scenario. Which is the better option?
Let's say they just use fair market rate for transactions.
Aug
3
asked Exchange Rate scenario. Which is the better option?
Jun
27
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Jun
3
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May
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Apr
23
asked Volumes of solids (of rotation). Any real world applications?
Apr
22
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Apr
18
comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital)
I'm not following what you did there,
Apr
12
accepted Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital)
Apr
12
comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital)
How did you introduce that division step? (Step 2 to Step 3)
Apr
12
comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital)
I don;t understand how that can be the solution, yet, the manual implies it's much more direct and obvious. Single worst "solution" I have ever seen in a book. You're just supposed to know how to split up the fraction like that?
Apr
12
comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital)
No clue what the tilda deal is, but there is no way that original explanation intended there to be any real work, or bizarre notation. Thanks for trying.
Apr
12
comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital)
What enrages me about the original explanation is that is so off-handedly implies the connection is obvious, and requires no actual work. There is no way in hell they intended the reader to be deriving all this stuff in these replies. Sadly, I still have absolutely no idea how lim sin(x)/x has anything to do with the 6x/2x problem. Sigh. Can someone please just spell it out for me, and please don't leave the last step out, all cute so I can finish. This has dragged on way longer than it should.
Apr
12
comment Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital)
Sorry, that was a typo. I corrected the correct solution above.
Apr
12
revised Not sure how to evaluate $\lim_{x\to 0}\frac{\sin6x}{\sin2x}$ (without l'Hospital)
edited body