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robinfr93
 2 years ago
Solve for Lim (10^X  1)/x
x>0
robinfr93
 2 years ago
Solve for Lim (10^X  1)/x x>0

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SithsAndGiggles
 2 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x\to0}\frac{10^{x}1}{x}?\] Examine the onesided limits. \[\lim_{x\to0^+}\frac{10^{x}1}{x}\] As x approaches 0 from the right, you'll be considering only positive values of x, which means x=x. \[\lim_{x\to0^+}\frac{10^{x}1}{x}=\frac{0}{0}\\ \text{Apply L'Hopital's rule}\\ \lim_{x\to0^+}\frac{\ln(10)\cdot10^{x}}{1}=\frac{\ln(10)}{1}=\ln(10)\] \[\lim_{x\to0^}\frac{10^{x}1}{x}\] As x approaches 0 from the left, you'll be considering negative values of x, which means x=x. \[\lim_{x\to0^}\frac{10^{x}1}{x}=\frac{0}{0}\\ \text{Apply L'Hopital's rule}\\ \lim_{x\to0^+}\frac{\ln(10)\cdot10^{x}}{1}=\frac{\ln(10)}{1}=\ln(10)\] Since the onesided limits aren't equivalent, the twosided limit does not exist.

robinfr93
 2 years ago
Best ResponseYou've already chosen the best response.0Well my text gives a different answer of 2.59. I stumbled upon the same answer but it says its wrong!! :(

SithsAndGiggles
 2 years ago
Best ResponseYou've already chosen the best response.0Have you tried putting ln(10) into a calculator? The textbook's answer is probably rounded.

robinfr93
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah its 2.3 something. Even if you round it off, there is no way it'll be 2.59

SithsAndGiggles
 2 years ago
Best ResponseYou've already chosen the best response.0It might also be the case that the textbook used an approximate method. \[\begin{matrix}\underline{x}& & &\underline{f(x)}\\ 1& & &9\\ 0.1& & &2.58925& & &\text{(probably stopped here)}\\ 0.01& & &2.3293\\ \vdots\end{matrix}\] \[\begin{matrix}\underline{x}& & &\underline{f(x)}\\ 1& & &9\\ 0.1& & &2.58925& & &\text{(again, probably stopped here)}\\ 0.01& & &2.3293\\ \vdots\end{matrix}\]

robinfr93
 2 years ago
Best ResponseYou've already chosen the best response.0@SithsAndGiggles Hmmm.. Could be.. Anyways thanx for helping.. I really appreciate it.. just for that I'll give you a medal, would had knighted you to Sir. SithsAndGiggles if had gotten a sure answer.. Anwys thanx again
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