Using L'Hopital's Rule
Read this topicExplanations 5
- Indeterminate forms also include ∞∞\frac{\infty}{\infty}∞∞, 0⋅∞0 \cdot \infty0⋅∞, ∞−∞\infty - \infty∞−∞, 000^000, 1∞1^\infty1∞, and ∞0\infty^0∞0. But here, we will be concerned…
By Ahaan Rungta
- Created by the Bernoulli brothers and named after Guillaume de l'Hospital, l'Hospital's Rule is a helpful tool when a limit of the form limx→af(x)g(x)\lim_{x\to a}\frac{f(x)}{g…
By Noah Libby, Japheth Wood, Victor Wang, Alex Federspiel
- (Video) L'Hospital's Rule for Indeterminate Products by PatrickJMT Here's a video by patrickJMT showing you how to use l'Hospital's rule to evaluate limits in the indeterminate …
By Alex Federspiel
- (Video) L'Hospital's Rule for Indeterminate Quotients by PatrickJMT Here's a video by patrickJMT where he explains l'Hospital's rule and shows you how to use it to solve limits …
By Alex Federspiel
- (Video) L'Hospital's Rule for Indeterminate Differences by PatrickJMT Here's a video by patrickJMT showing you how to use l'Hospital's rule to evaluate limits with indeterminate…
By Alex Federspiel
Problems 10
- Find the limit limx→0x21−cosx\lim_{x\to0} \frac{x^2}{1 - \cos{x}}limx→01−cosxx2. Source: HMMT February 2007
- Compute limx→2x−2x2−4\displaystyle \lim_{x\to2} \frac{x-2}{x^2-4}x→2limx2−4x−2.
- Compute limx→0tan5xsin3x\displaystyle \lim_{x\to0} \frac{\tan 5x}{\sin 3x}x→0limsin3xtan5x.
- Compute limx→4+x−4ln(2x−7)\displaystyle \lim_{x \to 4^+} \frac{x-4}{\ln(2x-7)}x→4+limln(2x−7)x−4.
- Compute limx→0xarctan(3x)\displaystyle \lim_{x\to 0} \frac x{\arctan(3x)}x→0limarctan(3x)x.
- Compute limx→∞x⋅e−x\displaystyle \lim_{x \to \infty} \sqrt x \cdot e^{-x}x→∞limx⋅e−x.
- Compute limx→∞xtan(1x)\displaystyle \lim_{x \to \infty} x \tan \left( \frac1x \right)x→∞limxtan(x1).
- Compute limx→0sinxx.\displaystyle \lim_{x\to 0} \frac{\sin{x}}{x}.x→0limxsinx.
- Let f(x)f(x)f(x) be a continuously decreasing function on (−∞,+∞)(-\infty, +\infty)(−∞,+∞). Also let f(x)+f′(x)=0f(x) + f'(x) = 0f(x)+f′(x)=0 and f(0)=1f(0) = 1f(0)=1. Compute l…
- limx→0ex−1x=?\lim _{x\rightarrow 0}\frac{e^x-1}{x}=?x→0limxex−1=?