Repeatedly Applying L'Hopital's Rule
Read this topicExplanations 3
- Sometimes for a particularly stubborn limit, one application of L'Hospital won't be enough, and we'll need to simply run it again and again, until we get something we can evalua…
By Calvin Lee, Alex Federspiel
- Sometimes you will need to use L'Hopital's more than once to get the answer. We know exe^xex grows "much faster" than x3x^3x3 so the numerator goes to infinity much faster than …
By Ray Li
- Explanation #1122
By Ahaan Rungta, Nikhil Kalghatgi, Moor Xu
Problems 3
- Compute limx→∞(lnx)2x\displaystyle \lim_{x\to\infty} \frac{(\ln x)^2}xx→∞limx(lnx)2.
- (Stanford Math Tournament 2008 Calculus #4) Find the value of the nnnth derivative of f(x)=sinnxf(x) = \sin^n xf(x)=sinnx (the nnnth power of the sine function) at x=0x = 0x=0.
- Evaluate: limx→∞(1+2x+3x)1x\lim_{x\rightarrow\infty}(1+2^{x}+3^{x})^{\frac{1}{x}}x→∞lim(1+2x+3x)x1