Graphical limit at point discontinuityYouTube↗  IA↗(long shot)
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- [Voiceover] So, here we have the graph y is equal to g of x.
Máme graf funkce y se rovná g(x).
We have a little point discontinuity right over here at x is equal to seven,
Máme zde malý bod nespojitosti a to v bodě x rovno 7.
and what we want to do is figure out what is the limit of g of x as x approaches seven.
A to, čeho chceme dosáhnout, je najít limitu g(x) pro x jdoucí k 7.
So, since you say, well, what is the function approaching as the inputs in the function are approaching seven?
Zeptejme se: "Čemu se blíží funkce, když se její vstupy blíží k 7?"
So, let's see, so if we input as the input to the function
Pokud dáme funkci na vstup…
approaches seven from values less than seven,
Když se blížíme k 7 zleva, tedy z hodnot menších než 7…
so if x is three, g of three is here, g of three is right there, g of four is right there, g of five is right there, g of six looks like it's a little bit more than,
Když x je 3, g(3) je tady, g(4) je přesně tady, g(5) je tady. g(6) vypadá, že je o trošku víc než to neboli o něco méně než -1.
or a little bit less than negative one,
g of 6.5 looks like it's around negative half,
g(6,5) vypadá, že bude kolem -0,5,
g of negative 6.9 is right over there, looks like it's a little bit less than zero,
g(6,9) je přesně tady, je to o trochu méně než 0.
g of negative 6.999 looks like it's a little bit, it's still less than zero but it's a little bit
g(6,999) je zase o trošku menší než 0, ale ještě o trochu blíže k ní…
closer to zero so it looks like we're getting closer as x gets closer and closer but not quite at seven,
Takže jak se blížíme… Jak se x stále víc a víc blíží, ale nikdy úplně, k 7,
it looks like the value of our function is approaching zero.
hodnota naší funkce se blíží k 0.
Let's see if that's also true from values for x values greater than seven,
Podívejme se, zda to platí i pro hodnoty x větší než 7.
so g of nine is up here, looks like it's around six,
g(9) máme tady nahoře, vypadá že je kolem 6.
g of eight looks like it's a little bit more than two,
g(8) vypadá, že je o něco více než 2.
g of 7.5 looks like it's a little bit more than one,
g(7,5) vypadá, že je o něco více než 1.
g of 7.1 looks like it's a little bit more than zero, the g of 7.1 looks like it's a little bit more than zero,
g(7,1) vypadá, že je o něco více než 0.
g of 7.01 is even closer to zero,
g(7,01) je ještě blíže k 0.
g of 7.0000001 looks like it'll be even closer to zero
g(7,0000001) bude ještě o něco blíže k 0,
so once again it looks like we are approaching zero
takže znova to vypadá, že se blížíme k 0, když se x blíží k 7.
as x as approaches seven, in this case as we approach from larger values of seven.
V tomto případě se blížíme z hodnot větších než 7.
And this is interesting because the limit as x approaches seven of g of x is different than
A to je zajímavé, protože limita g(x) pro x jdoucí k 7
the function's actual value, g of seven, when we actually input seven into the function.
je jiná než pravá hodnota funkce g(7), když vložíme 7 do naší funkce.
When we actually input seven into the function, we can see the graph tells us that the value of the function
Když vložíme 7 do naší funkce, vidíme, že graf nám říká,
is equal to three.
že hodnota funkce je rovna 3.
So we actually have this point discontinuity, or sometimes called a removable discontinuity,
Takže tady máme tento bod nespojitosti, nazývaný také odstranitelná nespojitost.
right over here, and this is, I'm not gonna do a lot of depth here, but this is starting to touch on how we,
A to je, nepůjdu moc do hloubky, ale narážíme na problém, jak můžeme…
one of the ways that we can actually test for continuity
Jedna z možností jak zkontrolovat spojitost funkce je,
is if the limit as we approach a value is not the same
že pokud se limita, jak se blížíme k nějaké hodnotě,
as the actual value of the function of that point,
není stejná jako hodnota funkce v tom bodě.
well, then we're probably talking about, or actually we are talking about, a discontinuity.
Potom se bavíme o nespojitosti funkce.
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