Let's go khổng lồ definitions. What does it mean for lim_x oinftyf(x) to lớn exist? It means that there exists some Lin mathbbRcup-infty, infty such that for any sequence (x_n) (where ...

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https://math.stackexchange.com/questions/1819265/taking-the-limit-lim-x-to-infty-x-tan1-x-without-lhopitals-rule
If you are allowed to use the fact that lim_t o0fracsin(t)t=1, then setting t=frac1x yields lim_x oinftyxsinBig(frac1xBig)=lim_x oinftyfracsin(frac1x)frac1x=lim_t o 0fracsin(t)t=1
displaystyle5 Explanation: displaystylex anleft(frac5x ight)=5frac anleft(frac5x ight)left(frac5x ight)making nowdisplaystyley=frac5x ...
We have lớn use thatdisplaystylelim_x o0fracsinxx=1to solve the indetermination Explanation:let's manipulate the expression a little bit first: displaystylelim_x o0left(frac anleft(fracx3 ight)x ight)=lim_x o0left(fracfracsinleft(fracx3 ight)cosleft(fracx3 ight)x ight)=lim_x o0left(fracsinleft(fracx3 ight)cosleft(fracx3 ight)x ight) ...
https://math.stackexchange.com/questions/2279752/what-is-the-limit-of-this-formula-lim-x-to-infty-arctan-x-pi-2x
lim_x o infty (arctan x -pi/2)x = lim_x o infty frac(arctan x - pi/2)frac1x This is the indeterminate form 0/0. Therefore, we can apply l'Hopital's rule. = lim_x o infty fracfrac11+x^2frac-1x^2 ...

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https://math.stackexchange.com/questions/690018/how-to-calculate-the-undefined-limit-of-this-trig-function
(x-2) andfracpi x=sindfracpi xcdotfracx-2cosdfracpi x extNow as cosdfracpi x=sinleft(fracpi2-fracpi x ight)=sinfracpi(x-2)2x, implies(x-2) andfracpi x=sindfracpi xcdotfracdfracpi(x-2)2xsindfracpi(x-2)2xcdotfrac2xpi ...
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left< eginarray l l 2 & 3 \ 5 và 4 endarray ight> left< eginarray l l l 2 & 0 & 3 \ -1 & 1 & 5 endarray ight>

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