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urur
@urur
September 2021
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Найти пределы.
Попутно объясните, как это делать, пожалуйста
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Lesben
1)lim (3x²/(x+1) - 3x)=lim (3x²-3x²-3x)/(x+1)=lim(-3x/(x+1)=
x→∞ x→∞ x→∞
=lim (-3+3/(x+1)=-3
x→∞
2)lim(x-4)/(√x -2) = lim (x-4)(√x+2)/(√x-2)(√x+2)=
x→4 x→4
=lim(x-4)(√x+2)/(x-4)=lim (√x+2)=2+2=4
x→4 x→4
3)lim sin5x/10x = 1/2.lim sin5x/5x=1/2.1=1/2
x→0 x→0
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Answers & Comments
x→∞ x→∞ x→∞
=lim (-3+3/(x+1)=-3
x→∞
2)lim(x-4)/(√x -2) = lim (x-4)(√x+2)/(√x-2)(√x+2)=
x→4 x→4
=lim(x-4)(√x+2)/(x-4)=lim (√x+2)=2+2=4
x→4 x→4
3)lim sin5x/10x = 1/2.lim sin5x/5x=1/2.1=1/2
x→0 x→0