Calculo de limites

EJERCICIO 1
1. -------------------------------------------------
F(x) = (x²-4)/(x²-5x+6) a=2
F(x) = x²-4x²-5x+6 =FACTORIZANDOx+2(x-2)x-2(x-3)

F(x) =X+2X-3 →2+22-3=4-1= -4

limX→2FX=-4
2. -------------------------------------------------
F(x) = (x³-2X-1)/(x+2) a=3

F(x) = 33+23-13+2 = 27+6-15 =33-15= 325

3. -------------------------------------------------
F(x) =(x³+1)/(x+1) a=-1
X²-x +1
X+1 x³ +1
-x³ -x²
-x² +1
+x²+x
-x +1
+x -1
0
F x = x² - x + 1a = -1

Fx = (-1)² - (-1) + 1 = 1 + 1 + 1 a = 3





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4-F(x) → (X+2-2)/(x-2) a=2

X+2-2X-2 *X+2+2X+2+2=X+2+2X+2-4X-2(X+2+2

=X+2-4X-2(X+2 +2)=X-2X-2(X+2+2)

f:x = 1X+2 +2 a=2

12+2+2=14 +2= 12+2=14
limx→21x+2+2=14-------------------------------------------------
5. F : → (2x+3-x)/(x-3) a=3

2x+3-xX-3 *2X+3+x2x+3+x=2x+3+x2x+3-x2x+3-x²X-3(2x+3+x)=(-1)(-1)

2x+3-xX-3 *2X+3+x2x+3+x= x²-2x-3-x-3(2x+3+ x)

2x+3-xX-3 *2X+3+x2x+3+x= x-3(x+1)x-3(2x+3+x)
2x+3-xX-3 *2X+3+x2x+3+x= -x+12x+3+x

2x+3-xX-3 *2X+3+x2x+3+x= -3+12(3)+3+3=-46+3+32x+3-xX-3 *2X+3+x2x+3+x= -46=-23
limx→3-x+12x+3+x=-23

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6. F : → (x-9)/(x-3) a= 9x-9x-3 *x+3x+3=x-9x +3x+3x -33-9

x-9x-3 *x+3x+3=x-9x +3x-9

x-9x-3 *x+3x+3=x+3

x-9x-3 *x+3x+3=9+3=3+3=6

limX→9x+3=6

EJERCICIO 2-------------------------------------------------
1.limX→3(X2+4X-6)=32+43-6
limX→3(X2+4X-6)=9+12-6
limX→3(X2+4X-6)=15

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2.limX→4(X²-16X-4)=X-4(X+4)X-4=X+4= 4+4= 8...