Table of Contents
T17
Pomocí l’Hospitalova pravidla vypočítejte limity:
199.
\( \lim_{x \to 0} \frac{\sin ax}{\sin bx} \) limit sin ax / sin bx as x-> 0
200.
\( \lim_{x \to 0} \frac{\cosh x - \cos x}{x^2} \) limit (cosh x - cos x)/x^2 as x->0 derivative cosh x sinh, použít pravidlo dvakrát!!!
201.
\( \lim_{x \to 0} \frac{\tan x - x}{x - \sin x} \)
limit of (tan x - x)/(x - sin x) as x->0
202.
\( \lim_{x \to 0} \frac{3 \tan 4x - 12 \tan x}{2 \sin 4x - 12 \sin x} \)
limit (3 tan 4x - 12 tan x)/(3 sin 4x - 12 sin x) as x->0
\( \lim_{x \to 0} \)
203.
\( \lim_{x \to \frac{\pi}{2}} \frac{\tan 3x}{\tan x} =1/3 \), použít 3krát!
limit tan 3x / tan x as x->pi/2
204.
\( \lim_{x \to 0} \frac{x \cot x - 1}{x^2} \)
205.
\( \lim_{x \to \frac{\pi}{4}} \frac{\sqrt[3]{\tan x} - 1}{ 2 \sin^2 x - 1} \)
206.
\( \lim_{x \to 0} \frac{x(e^x + 1) − 2(e^x − 1)}{x^3} \)
207.
\( \lim_{x \to 0} \frac{1 − \cos x^2}{x^2 sin x^2} \) limit (1 − cos x^2) / (x^2 sin x^2) as x->0
208.
\( \lim_{x \to 0} \frac{a^x - \a^{\sin x}}{x^3} \)
209.
\( \lim_{x \to 1} \frac{x^x - x}{\ln x - x + 1} \) limit (x^x - x) / (ln x - x + 1) as x->1
210.
\( \lim_{x \to 0} \frac{\ln \sin ax}{\ln \sin bx} \)
limit of (ln sin ax)/(ln sin bx) as x->0
211.
212.
\( \lim_{x \to +\infty} \frac{x^n}{e^{ax}}, a>0, n>0 \) limit x^n/e^(ax) as x->+oo
213.
\( \lim_{x \to 0} \frac{e^{-\frac{1}{x^2}}}{x^100} \) limit e^{-1/x^2 / x^100 as x->0
214.
215.
\( \lim_{x \to 1-} (ln x)(ln(1 - x) \) limit of (ln x)(ln(1 - x) as x->1-
216.
\( \lim_{x \to +0} x^a\ln x , a>0 \)
limit x^a ln x as x->+0
217.
\( \lim_{x \to +0} x^x \) limit x^x as x->+0 derivative x^x T217
218.
\( \lim_{x \to 0} x^(x^x - 1) \)
limit x^(x^x - 1) as x->0
219.
\( \lim_{x \to 0} x^{x^x} - 1 \) limit of x^x^x -1 as x->0
220.
\( \lim_{x \to +0} x^\frac{k}{1 + ln x} \)
221.
\( \lim_{x \to 1} x^\frac{1}{1 - x} \) limit x^(1/(1 - x)) as x->1 T221
222.
223.
224.
\( \lim_{x \to 0} (\cot x)^{\sin x} \)
limit of (cotg x)^sin x as x->0
225.
\( \lim_{x \to 0+} (\ln \frac{1}{x})^x \) limit of (ln 1/x)^x as x->0+ T225
226.
227.
228.
\( \lim_{x \to 1} ( \frac{1}{\ln x} - \frac{1}{x -1}) \) limit ( 1/ln x - 1/(x - 1) ) as x->1
229.
