Exercicios de limites
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3 páginas
01 - limx→1 3x2+3x-6x2+2x-3Adotando 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 . 29-1 lim 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→∞ x3 1,70 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+1 limx→∞ 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+1 limn→∞ -1 0
11 – lim x→2++ x2 . 2 x . 2
Adotando → x=2+ 1n logo teremos
limn→∞ 2+ 1n-2 2+ 1n- 2 limn→∞