Lim (1 + 3/x)^5x
x→∞
lim(1+k/x)^x = e^k
x→∞
lim (1 + 3/x)^5x=lim(1+ 3/x)^x*lim(1+ 3/x)^x*lim(1+ 3/x)^x*lim(1+ 3/x)^x*lim(1+ 3/x)^x
= e^3*e^3*e^3*e^3*e^3=e^15
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lim ((x-2)/√(x+2) -2)⇒ (x-2)/√(x+2) при x→2 стремится к 0
x→2
lim ((x-2)/√(x+2) -2) = -2
x→2
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lim (x²- 3x)/(x²- 8) = 1
x→∞
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lim (tg(x/3)/x) = lim (sin(x/3)/cos(x/3)/x) = lim (sin(x/3)/(xcos(x/3))
x→0 x→0 x→0
sin(x/3) при x→0 стремится к х/3
cos(x/3) при x→0 стремится к 1
lim (x/3/x) = 1/3
x→0