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TAREA LIMITES DE MATEMATICA
Límites:
1.
limx→12x2-144x-12
limx→12x+12(x-12)x-12
limx→12 x+12=24

2.
limx→122x2-15x+72x2+13x-7
limx→122x-1(x-7)2x-1(x+7)
limx→12-132152= -1315

3.limx→139x2-13x2+2x-1
limx→133x+1(3x-1)3x-1(x+1)
limx→13243= 32

4.
limx→7x3-4x2-19x-14x2-8x+7
limx→7x+1(x2-5x-14)x-7(x-1)
limx→7(x+1)(x-7)(x+2)x-7(x-1)
limx→7(x+1)(x+2)(x-1)
limx→712

5.limx→1x3-4x2-19x-14x2-8x+7
limx→1x-1(x2+2x-3)x-1(x2+3x-4)
limx→1(x-1)x+3(x-1)x-1x+4(x-1)
lim⁡ x→145
6.
limx→1x4-3x+2x5-4x+3
limx→1x-1(x3+x2+x-2)x-1(x4+x3+x2+x-3)
limx→11+1+1-21+1+1+1-3
limx→1=1

7.limx→1-x5-2x4+3x3-6x2+2x+4x4-3x3-7x2+27x-18
limx→1x-1(-x4-3x3-6x-4)x-1(x3-2x2-9x+18)
limx→1-1-3-6-412-2-9+18
limx→1-72
8.
limx→1x17+x15-22x3-x5-1
limx→1x-1(x16+x15+2x14…+2x+2)x-1(-x4-x3+x2+x+1)limx→11+1+2*14+2-1-1+1+1+1
limx→1=32

9.
limx→1x13-1x78-1
limx→1x13x-1x78x-1
limx→1x12+x11+…+1x77+x76+…+1
limx→1=1378
10.
limx→1x200-x100+x2-1x100+x20-x5-1limx→1x200-1x-1-x100-1x-1+x2-1x-1x100-1x-1+x20-1x-1-x5-1x-1
limx→1x199+x198+…+1-x99+x98…+1+(x+1)x99+x98…+1+x19+...x+1-(x4+x3…+1)
limx→1200-100+2100+20-5
limx→1=102115

11.
limx→0x-1x+12x-1-1x
limx→02x3-x2-2xx
limx→02x2-x-2limx→0= -2

14.
limx→1x2+3x-4x+3-2
limx→1x+4x-1x+3+2(x+3-2)x+3+2
limx→1x-4(x-1)x+3+2(x-1)
limx→1x+4(x+3+2)
limx→1=20
15.
limx→15x-17x-1
x=yMCM(7,5)= y35
limx→1y7-1y5-1
limx→1y7-1y-1y5-1y-1limx→1y6+y5+…+y+1y4+…+y+1
limx→1= 75

16.
limx→13x-1ax-1
x=yMCM(4,3)=y12
limx→1y4-1y3-1
limx→1y4-1y-1y3-1y-1
limx→1y3+y2+y+1y2+y+1
limx→1= 43

13. limx→13x-1x+3-2xx+3+2x+3+2limx→1(3x-1)(x+3+2)(x+3)2-(2)2
limx→1(3x-1)(x+3+2)x+3-4
(31-1)(1+3+2)1+3-4= 0.

17. limx→313+x-10+2x19+2x-5
13+x-10+2x19+2x-519+2x+519+2x+5
(13+x-10-2x)(√(19+2x)+5 19+2x-25
(13+x-10-2x)(√(19+2x)+52x-6x13+x+10-2x)13+x+10-2x)

limx→3(13+x-10-2x)(19+2x+5)2x-6(13+x+10-2x)
-(x-3)(19+2x+5)2(x-3)(13+x+10+2x)
limx→3-(19+2x+5)2(13+x+10-2x)
-(19+6+5)2(13+3+10-2(3))
-(25+5)2(16+16)=-1016=-58

19....