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    Derivada Implícita : Dy/Dx O Y

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    Renzo Andree Romani Chavez
    This document discusses three mathematical concepts: 1) Implicit differentiation (dy/dx or y'), showing an example of finding the derivative of an implicit equation. 2) L'Hopital's rule for evaluating limits that result in indeterminate forms like 0/0 or infinity/infinity. 3) Taylor polynomials for approximating functions as polynomials, including an example of finding the 3rd degree Taylor polynomial about x=1 for the function f(x)=x^(3/2).

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    Derivada Implícita : Dy/Dx O Y

    Uploaded by

    Renzo Andree Romani Chavez
    6 views3 pages
    This document discusses three mathematical concepts: 1) Implicit differentiation (dy/dx or y'), showing an example of finding the derivative of an implicit equation. 2) L'Hopital's rule for evaluating limits that result in indeterminate forms like 0/0 or infinity/infinity. 3) Taylor polynomials for approximating functions as polynomials, including an example of finding the 3rd degree Taylor polynomial about x=1 for the function f(x)=x^(3/2).

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    DERIVADA IMPLÍCITA

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    This document discusses three mathematical concepts: 1) Implicit differentiation (dy/dx or y'), showing an example of finding the derivative of an implicit equation. 2) L'Hopital's rule for evaluating limits that result in indeterminate forms like 0/0 or infinity/infinity. 3) Taylor polynomials for approximating functions as polynomials, including an example of finding the 3rd degree Taylor polynomial about x=1 for the function f(x)=x^(3/2).

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    6 views3 pages

    Derivada Implícita : Dy/Dx O Y

    Uploaded by

    Renzo Andree Romani Chavez
    This document discusses three mathematical concepts: 1) Implicit differentiation (dy/dx or y'), showing an example of finding the derivative of an implicit equation. 2) L'Hopital's rule for evaluating limits that result in indeterminate forms like 0/0 or infinity/infinity. 3) Taylor polynomials for approximating functions as polynomials, including an example of finding the 3rd degree Taylor polynomial about x=1 for the function f(x)=x^(3/2).

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 3

    DERIVADA IMPLÍCITA (DY/DX O Y´)

    6 x 3 y −2 y −3 y 3=4 x

    18 x 2 y +6 x 3 y ´ −2 y ´ −9 y 2 y ´=4

    y ´ ( 6 x 3−2−9 y 2 ) =4−18 x 2 y

    4−18 x 2 y
    y ´= 3
    6 x −2−9 y 2

    REGLA DE L´HOPITAL(0/0 o ∞/∞)

    1 1 lim sinx−x
     lim
    x →0
    ( −
    x sinx )  x→0
    x∗sinx
     se tiene la indeterminación 0/0  Aplicamos la regla

    de L´Hospital.

    lim sinx−x lim cosx −1


     x→0
     x →0
     se Vuelve a obtener la indeterminación 0/0 
    x∗sinx senx + xcosx
    Aplicamos la regla de L´Hospital.

    lim cosx −1 lim −sinx


     x →0  x→ 0 0
    = =0
    senx + xcosx cosx+cosx −xinx 2
    POLINOMIO DE TAYLOR

    f ´ (a) f ´ ´ (a) 2 f ´ ´ ´ (a) 3 f n( a) n


    Pn ( x )=f ´ ( a ) + ( x −a ) + ( x −a ) + ( x−a ) + ..... ( x−a )
    1! 2! 3! n!

    Grado 3, Xo = 1 de f(x) = x^ (3/2)

    f ´ ( 1) f ´ ´ (1 ) f ´ ´ ´ (1)
    P3 ( x ) =f ( 1 ) + ( x−1 ) + ( x−1 )2+ ( x−1 )3
    1! 2! 3!

    3
    f ( x )=x 2  f (1)=1
    1
    3 2 f ´ (1)= 3
    f ´ ( x )= x 
    2 2
    3 3
    f ´ ´ ( x )= 1  f ´ ´ (1)=
    4x 2 4

    −3
    f ´ ´ ´ ( x )= 3  f ´ ´ ´ ( 1 )=
    −3
    8x 2 8

    3 3 −3
    2 4 8
    P3 ( x ) =1+ ( x−1 )+ ( x−1 )2 + ( x−1 )3
    1! 2! 3!

    3 3 3
    P3 ( x ) =1+ ( x−1 )+ ( x−1 )2− ( x−1 )3
    2 8 24

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