VIDEO
El límite es un concepto que describe la tendencia de una sucesión o una función, a medida que los parámetros de esa sucesión o función se acercan a determinado valor.
Vídeo de explicación de limites algebraicos:
1)
Respuesta :{\displaystyle \lim _{x\to -2}{\frac {x(x+1)(x+2)}{(x+2)(x-3)}}} {\displaystyle \lim _{x\to -2}{\frac {x(x+1)}{x-3}}} {\displaystyle {\frac {-2(-2+1)}{-2-3}}} {\displaystyle {\frac {2}{-5}}} 2)
Respuesta :{\displaystyle \lim _{x\to 1}{\frac {x^{4}(1-x)}{1-x}}} {\displaystyle \lim _{x\to 1}x^{4}} {\displaystyle 1}
3)
RESPUESTA :evaluando :
{\displaystyle \lim _{x\to 0}{\frac {{\sqrt {(}}2-t)-{\sqrt {2}}}{t}}} =
{\displaystyle {\frac {{\sqrt {(}}2-0)-{\sqrt {2}}}{0}}} =
{\displaystyle {\frac {{\sqrt {2}}-{\sqrt {2}}}{0}}={\frac {0}{0}}}
{\displaystyle \lim _{x\to 0}{\frac {{\sqrt {(}}2-t)-{\sqrt {2}}}{t}}} =
{\displaystyle \lim _{x\to 0}{\frac {({\sqrt {(}}2-t)-{\sqrt {2}})({\sqrt {(}}2-t)+{\sqrt {2}}}{t({\sqrt {(}}2-t)+{\sqrt {2}}}}} =
{\displaystyle \lim _{x\to 0}{\frac {({\sqrt {(}}2-t))^{2}-({\sqrt {2}})^{2}}{t({\sqrt {(}}2-t)+{\sqrt {2}})}}} =
{\displaystyle \lim _{x\to 0}{\frac {(2-t)-2)}{t({\sqrt {(}}2-t)+{\sqrt {2}})}}} =
{\displaystyle \lim _{x\to 0}{\frac {-t}{t({\sqrt {(}}2-t)+{\sqrt {2}})}}} =
{\displaystyle \lim _{x\to 0}{\frac {-1}{{\sqrt {(}}2-t)+{\sqrt {2}}}}={\frac {-1}{{\sqrt {(}}2-0)+{\sqrt {2}}}}} =
{\displaystyle {\frac {-1}{{\sqrt {(}}2)+{\sqrt {2}}}}} =
{\displaystyle {\frac {-1}{2{\sqrt {2}}}}}
4)
Respuesta :
{\displaystyle lim_{x\to \infty }{\frac {2}{(1/x)+(1/x^{3})}}} {\displaystyle n.e}
5)
{\displaystyle \lim _{h\to 0}{\frac {{\sqrt[{2}]{x+h}}-{\sqrt[{2}]{x}}}{h}}} Respuesta :
{\displaystyle \lim _{h\to 0}{\frac {{\sqrt[{2}]{x+h}}-{\sqrt[{2}]{x}}}{h}}{\frac {{\sqrt[{2}]{x+h}}+{\sqrt[{2}]{x}}}{{\sqrt[{2}]{x+h}}+{\sqrt[{2}]{x}}}}} =
{\displaystyle \lim _{h\to 0}{\frac {h}{h({\sqrt[{2}]{x+h}}+{\sqrt[{2}]{x}})}}} =
{\displaystyle \lim _{h\to 0}{\frac {1}{{\sqrt[{2}]{x+h}}+{\sqrt[{2}]{x}}}}} =
{\displaystyle {\frac {1}{2{\sqrt {x}}}}}
=
=
=
=
=
=
=
![{\displaystyle \lim _{h\to 0}{\frac {{\sqrt[{2}]{x+h}}-{\sqrt[{2}]{x}}}{h}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c8eb733b5865bc78bfc00dd0c97bfd27974f737)
![{\displaystyle \lim _{h\to 0}{\frac {{\sqrt[{2}]{x+h}}-{\sqrt[{2}]{x}}}{h}}{\frac {{\sqrt[{2}]{x+h}}+{\sqrt[{2}]{x}}}{{\sqrt[{2}]{x+h}}+{\sqrt[{2}]{x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9e15cfdabf1d50ec2c899f8dda886374754cc786)
=![{\displaystyle \lim _{h\to 0}{\frac {h}{h({\sqrt[{2}]{x+h}}+{\sqrt[{2}]{x}})}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e7d4380381e3ade65dd3291607643688c5bff786)
=![{\displaystyle \lim _{h\to 0}{\frac {1}{{\sqrt[{2}]{x+h}}+{\sqrt[{2}]{x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/495efc10caa70f1e75f880d354dafc55a9edb5c3)
=
No hay comentarios:
Publicar un comentario