A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing

This Question is Closed

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
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.