Category: Limits

Question Number 1817 by 112358 last updated on 05/Oct/15 $$Evaluatethefollowinglimit,$$$$ifitexists,$$$$\underset{x\to 0}{\lim }\frac{sin\left(sin\left(sinx\right)\right)}{x}.$$ Answered by 123456 last updated on 05/Oct/15 $${f}_{{n}}…

Question Number 1767 by Rasheed Ahmad last updated on 18/Sep/15 $$Determine$$$$\left(i\right)\underset{a\to \mathrm{\infty }}{lim}{\left(\frac{1}{a}\right)}^a\left(ii\right)\underset{a\to 0}{lim}{\left(\frac{1}{a}\right)}^a$$ Answered by 123456 last updated on…

Question Number 1499 by 112358 last updated on 14/Aug/15 $$Usetheϵ-\delta definitionofthe$$$$limittoshowthat$$$$\underset{x\to 3}{\lim }\frac{x}{6-x}=1.$$$$(I^{\prime }mhopingtobetterunderstand$$$$thisconceptbyexamplesoplease$$$$helpmebyexplaningthe$$$$reasoningbehindyoursteps.)$$…

Question Number 132483 by abdullahquwatan last updated on 14/Feb/21 $$\underset{x\to -2}{\lim }\frac{\sqrt{x^2+2x+4}-x^2+2}{x^5+32}\mathrm{no}\mathrm{hospital}$$ Commented by EDWIN88 last updated on 14/Feb/21 $$\mathrm{what}\:\mathrm{hospital}? \…

Question Number 1368 by prakash jain last updated on 25/Jul/15 $$\underset{x\to \mathrm{\infty }}{\lim }\frac{\ln (ax+b)}{\ln (bx+a)}=?$$ Commented by 123456 last updated on 25/Jul/15 $$f\left(x\right)=\frac{\ln (ax+b)}{\ln (bx+a)}$$$$\frac{\frac{{d}}{{dx}}\left[\mathrm{ln}\:\left({ax}+{b}\right)\right]}{\frac{{d}}{{dx}}\left[\mathrm{ln}\:\left({bx}+{a}\right)\right]}=\frac{\frac{{a}}{{ax}+{b}}}{\frac{{b}}{{bx}+{a}}}=\frac{{a}\left({bx}+{a}\right)}{{b}\left({ax}+{b}\right)}\rightarrow\frac{{ab}}{{ba}}=\mathrm{1} \…