JackOfAll
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 12h accepted Does this one require integration by parts? 12h comment Does this one require integration by parts? Doh! Just a basic u-sub! OVERTHOUGHT THIS 14h asked Does this one require integration by parts? Apr 29 revised Why is this piece-wise limit equal to 2? added 220 characters in body Apr 29 accepted Why is this piece-wise limit equal to 2? Apr 29 comment Why is this piece-wise limit equal to 2? I did it like this: $$\lim\limits_{h \to 0^+} \frac{f(3+h)-f(3)}{h} = \lim\limits_{h \to 0^+} \frac{[2(3+h)-4]-2}{h} = \lim\limits_{h \to 0^+} \frac{6+2h-4-2}{h} = \lim\limits_{h \to 0^+} \frac{2h}{h} = 2$$ Apr 29 comment Why is this piece-wise limit equal to 2? It's f(3), not f(x).....So, I don't understand why you didn't evaluate f(3) in the numerator, and instead used (2x-4). Shouldn't it be: $$\frac{[2(x+h)-4]-3}{h}$$ Apr 29 comment Why is this piece-wise limit equal to 2? I think you missed the point of why I wrote f(3.0001). As h->0, the numerator is basically approaching f(3) - f(3), which is 0. The closer h gets to 0, yet stays positive, the closer the numerator gets to f(3) - f(3), because f(3+h) will map to the 2nd piece (2x-4)... which turns into 2-2.... Apr 28 asked Why is this piece-wise limit equal to 2? Apr 28 accepted Is this an incorrect error bound value? Apr 28 answered Is this an incorrect error bound value? Apr 15 comment Is this an incorrect error bound value? Glad I'm not missing something! Yes, the alternating was skipped also. Apr 13 asked Is this an incorrect error bound value? Mar 30 awarded Popular Question Mar 30 accepted converges or diverges? $\sum_{n=1}^\infty \sin^2(\frac{\pi}{n})$ Mar 29 accepted Why is $\lim_\limits{x\to 0}\frac{\sin(6x)}{\sin(2x)} = \frac{6}{2}=3$? Mar 29 comment converges or diverges? $\sum_{n=1}^\infty \sin^2(\frac{\pi}{n})$ Oh, that's right! Thanks Mar 29 comment converges or diverges? $\sum_{n=1}^\infty \sin^2(\frac{\pi}{n})$ Oh, right, $\frac{sin(x)}{x}$ I didn't recognize it in that "disguised form" ! But, the limit is going to infinity, not 0.,.... Mar 29 comment converges or diverges? $\sum_{n=1}^\infty \sin^2(\frac{\pi}{n})$ How did you get $1^2$ ? I get indeterminate form of $\frac{0}{0}$ Did you use L'hopitals ? Mar 29 asked converges or diverges? $\sum_{n=1}^\infty \sin^2(\frac{\pi}{n})$