Exercicios de limites

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  • Publicado : 23 de março de 2013
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01 -
limx→1 3x2+3x-6x2+2x-3

Adotando x=1+ 1n logo teremos

limn→∞ 31+1n2+ 31+1n -6 1+1n2+ 2 1+1n-3 lim n→∞ 9+ -3 2+ -6 lim n→∞6 -4 = -1,5

02 -
limx→1/3 3x2+2x-19x2-1

Adotando → x=13 + 1n logo teremos

limn→∞ 313+1n2+ 213+1n -1 9 13+1n2-1 lim n→∞ 3 . 19+2. 13-19 . 29-1lim n→∞ 39+23-1189-1

lim n→∞ 39+23-11 lim n→∞ 39+69-1 1 lim n→∞ 99-11 = 01

03 -
limx→1 x2-1x2- x

Adotando →x=1+ 1n logo teremos

limx→∞ 1+1n2-11+1n2-1+1n lim n→∞ 1-11-1 = 0

04 –

limx→1 2- x2-1 x-1

Adotando → x=1+ 1n logo teremos

limx→∞2-1+1n2-11+ 1n-1 limx→∞ 2-1-1 1-1= 00

05 –

limx→∞ 35x3-2 7x limx→∞ x3 35x3x3 - 2x33 x 7xx limx→∞ x3 35 x 7 limx→∞ x31,70 x 7

limx→∞ x2.0,242=∞ x→+∞

06 -
limx→+∞ 3x7-x105x15-x10 limx→+∞ x10 3x7x10-1x15 5- x10x15 limx→+∞ x10-1x15-5 = x-5 -15 = ∞07 –
limx→∞ 5x 45x4+3 limx→∞ x 5x x4 45+3x4 limx→∞ x 5 x4 1,49 limx→∞ x-3 5 1,49 = ∞

08 –
limx→∞ 6x3+5x2-7x+34x3-5x+1limx→∞ x3 6 +5x2x3-7xx3+3x3x3 4- 5xx3 + 1x3 limx→∞ x3 6 x3 4 = 1,5

09 –
limx→0 x2x limx→0 x2x limx→0 x2 1x 1 limx→0 x .1= 0

10 –
limx→1 2x-2 x2-2x+1


Adotando → x=1+ 1n logo teremos

limn→∞ 21+ 1n -2 1+1n2-2 1+1n+1 limn→∞ 21 -2 1-2+1limn→∞ -1 0

11 –
lim x→2++ x2 . 2 x . 2

Adotando → x=2+ 1n logo teremos

limn→∞ 2+ 1n-2 2+ 1n- 2 limn→∞...
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