limita- prosím o pomoc
a) limita x->∞ (x*sinx)/x
b) limita x->π ln(1+cosx)
c) limita x->-∞ (√x na 2+1)/x
b) limita x->π ln(1+cosx)
c) limita x->-∞ (√x na 2+1)/x
Odpovědi
Diskuze
limita x->∞ (sinx)/x
https://socratic.org/questions/how-do-you-determine-the-limit-of-sin-x-x-as-x-approaches-infinity
lim (x->∞) (sinx)/x = 0
b) limita x->π ln(1+cosx)
cos(π)=-1
lim (x->π) ln(1+cosx) =
lim (x->π) ln(1-1) =
lim (x->π) ln(0) =
= -∞
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https://www.wolframalpha.com/input/?i=limita+x-%3E%CF%80+ln(1%2Bcosx)
c) nerozumím zadání
c) limita (x->-∞) √(x²+1) / x
lim (x->-∞) √(x²+1) / x = +∞/-∞ (znaménko bude záporné)
lim (x->-∞) (-1)*√(x²+1) / √(x²) =
lim (x->-∞) (-1)*√(1+1/x²) = (-1)*|1|, znaménko bude záporné
= -1
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https://www.wolframalpha.com/input/?i=limita+(x-%3E-%E2%88%9E)+%E2%88%9A(x%C2%B2%2B1)+%2F+x