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Plantilla para goma 5

                  f(x)=e^x(x-2) noA.V. ni A.H(+∞)     y=0   A.H en (-∞)

         limf(x)x→-∞=limx→+∞ (-x-2)/e^x=∞/∞  L'H  limx→+∞=1/∞=0

f'(x)=e^x(x-2) +e^x(1)=e^x(x-1) f'(x)=0 (x-1)=0 e^x no se anula nunca

          f'(0)=<0 decrec="">0><1 >1 >'(2)=>0 crec x>1x=1min relat =-e

  f''(x)=e^x(x) f''(-1)=<0 concav="">0><0>0>''(1)=>0 convex x>0 f(0)=-2

                      a)

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Plantilla para goma 5

                           a y b   fx=ax²+blnx   f'(1)=0  f(x)=ax²+bln(x)

                                             f'(x)=2ax + b/x   2a+b=0  b=-2a

                                                                         f(x)=ax²-2alnx

                  ∫⁴1f(x)dx=27-8ln(4)  ∫⁴1 (ax² - 2aln(x))dx=27-8ln(4)=

             =...

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Plantilla para GOMA 5

f(x)=x²-8lnx  f'(x)derivabl n(0,∞)  f'(x)=2x-(8/x)=0→x=-2(no) x=2

                                f'(1,5)=2(1,5)-(8/1,5)=-2,3<0 decrec="">0>

                                  f'(2,5)=2(2,5)-(8/2,5)=1,8>0 crecient (2,e)

f(1)=1-0=1  f(e)=0,61  f''(x)=2+(8/x²) f''(2)=2+2=4>0convex(1,e)

            f(x)=x³-4x  f(1)=1³-4=-3    f'(x)=3x²-4   f'(1)=3(1)²-4=-1

    y+3=-1(x-1)=x+1  y=-x-2    limf(...

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Plantilla para GOMA 5

                 HF + H20 ↔ F^- +  H3O⁺          (concentr) Ca: 0,0010 mol/L (M)              Ka(HF)=10^-3,25

equilibrioCa-x              x        x     Ka=[F^-]·[H3O⁺]/[HF]   ;  10^-3,25=(x · x)/(0,001 - x)=x²/10^-3      x²=10^-6,25-10^-3,25·x

                                                       x²+10^-3,25·x-10^-6,25=0    x=[-10^-3,25+√(10^-3,25)2+4·10^-6,85]/2= 5,2·10-...

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Plantilla para GOMA 5

 NaCN(s) → Na⁺  +  CN^-     0,01mol  Ka(HCN)=10^-9,31           Csal=0,01mol/1L=0,01M       Ka(HCN)·Kb(CN-)=Kw

0,1mol/L         0,1mol/L           Kb(CN-)= Kw/Ka(HCN)= [HCN][HO^-]/[CN^-]=10^-14/10^-9,31=10^-4,69

 CN- +  H2O ↔ HCN + HO-          10^-4,69=x·x/0,01-x ≈ x²/0,01 → x²=10^-4,69·10^-2=10^-6,69       x=(10^-6,69)^½=10^-3,345

0,01-x             x         x              x=[HO^-]=10^-3,345mol/L     pOH=...

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Plantilla para GOMA 5

 a) 50 mL d HCl 0,01M HCl + H2O ↔(100% α=1)↔ Cl^- + H3O⁺ →[H3O⁺]=Ca=10^-2M pH=-log[H3O⁺]=-log·10^-2=2

b) 50 mL d Ba(OH)2 0,01M     Ba(OH)2      ↔      Ba²⁺ +   2OH^-             [OH^-]=2Cb=0,02mol/L

                                         Cb=0,01mol/L         0,01      2x0,01mol/L   pOH= -log[HO-]=1,7    pH=14-pOH=12,3

c) pHmezcla? 2HCl + Ba(OH)2 ↔ BaCl2 + 2H2O -ΔnHCl/2=-ΔnBa(OH)2/1

           ...

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Plantilla para GOMA 5

                 HF + H20 ↔ F^- +  H3O⁺          (concentr) Ca: 0,0010 mol/L (M)              Ka(HF)=10^-3,25

equilibrioCa-x              x        x     Ka=[F^-]·[H3O⁺]/[HF]   ;  10^-3,25=(x · x)/(0,001 - x)=x²/10^-3      x²=10^-6,25-10^-3,25·x

                                                  x²+10^-3,25·x-10^-6,25=0    x=[-10^-3,25+√(10^-3,25)2+4·10^-6,85]/2= 5,2·10-4

α=(...

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Plantilla para GOMA 5

 Rect tg  f(x)=X³-4 |  f(x)=f'(a)·(x-a)+f(a)  |    a=1 (x=1)  

f'(x)=3x²-4              f'(1)=3·1²-4=-1          f(1)=1³-4=-3 

f(x)=-1·(x-1)+(-3)     f(x)=-x+1-3               f(x)=-x-2

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Calc A y B    -x²+bx+1   si x≤1      lim -1 + b + 1= b

            f(x)                                      x→1-

             ...

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Plantilla para GOMA 5

                              Asíntot    f(x)=(3x⁴+1)/x³       x≠0

                                                    lim=1/0^-=-∞

                          A.Vertical x=0    x→0-

                                                   lim=1/0⁺=+∞

                                             ...

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