Graphical limit where function undefinedYouTube↗  IA↗(long shot)
Education  263.3K views 40 likes 4 dislikes   11 Jul 2016
Khan Academy 9.4M subscribers United States YouTube↗


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Portuguese Mairon Oliveira de Lima
Korean yk k
French Hadrien Lacroix
Chinese (China) g chen
yang yi
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so we have the graph of y equals f of X
Máme tady graf funkce y se rovná f(x).
right over here and what we want to do is figure out the limit of f of X as X approaches negative
A chceme najít limitu f(x) pro x jdoucí k -4.
4 so what does that mean well a limit is
Co to znamená?
saying what is my function approach as the input of that function approaches in
Limita nám říká "K čemu se blíží moje funkce, když se její vstup
this case negative 4 as the input approaches a value and as we see in this
přibližuje, v tomto případě -4? Když se vstup blíží k hodnotě?"
example the function doesn't necessarily
A jak vidíme v tomto příkladu, funkce nemusí ani nutně být definovaná
have to be even defined at that value we
v té dané hodnotě.
can see F of negative 4 you go to x equals negative 4 and you see that F of
Vidíme f(-4), jdeme k x se rovná -4.
negative 4 is undefined so this is not
A vidíme, že f v bodě -4 není definovaná.
defined but as we'll see even though the
Toto tedy není definováno, ale ukážeme si,
function isn't defined there the limit might be defined there and actually it
že přestože samotná funkce tam není definovaná, její limita může.
could go the other way around
A může tomu být i naopak.
sometimes a function is defined there but the limit is not and we'll see that in future videos but let's just get an
Někdy je funkce definovaná, ale limita ne a na to se podíváme v dalších videích.
understanding here what's going on as X
Ale zaměřme se na správné pochopení situace.
approaches negative 4 as X approaches
Co se stane, když se x blíží k -4?
negative 4 from values greater than negative 4 and from values less than negative 4 well let's first think about
Z hodnot větších než -4 a z hodnot menších než -4.
values greater than negative 4 so when X
Napřed hodnoty větší než -4.
is negative 1 this is f of negative 1
Když je x rovno -1, toto je f(-1).
this is f of negative 2 this is f of
Toto je f(-2), toto je f(-3).
negative 3 this is F of negative 3 point
Toto je f(-3,5).
5 this is F of negative 3 point 9 this
Toto je f(-3,9).
is F of negative 3 point 9 9 this is F of negative 3 point 9 9 9 9 9 9 and so
Toto je f(-3,99), toto je f(-3,999999).
you can see the value of our function as X gets closer and closer to negative 4
Můžete vidět, že hodnota naší funkce, když se x víc a víc blíží k -4,
from values greater than negative 4 seems to be approaching 6 and let's see
z hodnot větších než -4, nejspíš bude 6.
if that's true from the other direction
Podívejme se, zda to platí
some from values less than negative 4 so
i z druhého směru, tedy od hodnot menších než -4.
this is f of negative 7 f of negative 6
Takže toto je f(-7), toto je f(-6).
this is f of negative 5 looks around 7
Toto je f(-5), dává nám něco kolem 7.
this is F of negative 4 point 5 F of negative 4 point 1 F of negative 4 point
Toto je f(-4,5), toto f(-4,1),
0 1 F of negative 4 point 0 0 0 0 1 it
toto f(-4,01), toto f(-4,000001),
looks like it's getting awfully it's
začíná to vypadat hrozivě, bude to o malinko víc než 6,
going to be a little bit more than 6 so it seems as we get closer and closer to 6 as we get closer and closer to x
takže když se dostáváme blíž a blíž k x se rovná -4,
equals negative 4 the value of our function is approaching positive six
tak se hodnota naší funkce blíží k +6.
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