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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}) $