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Find the indicated limit, if it exists. limit of f of x as x approaches negative 5 where f of x equals x plus 4 when x is less than negative 5 and f of x equals 4 minus x when x is greater than or equal to negative 5

Respuesta :

konrad509

[tex] \displaystyle
f(x)=\begin{cases} x+4, & x<-5\\4-x, &x\geq-5 \end{cases}\\\\\\
\lim_{x\to -5^-}(x+4)=-5+4=-1\\
\lim_{x\to -5^+}(4-x)=(4-(-5))=9\\\\
[/tex]


[tex] \displaystyle
\lim_{x\to -5^-}\not =\lim_{x\to -5^+} [/tex] so limit doesn't exist.

The limit does not exist.

Limit:

  • The value that a function (or sequence) approaches as the input (or index) approaches a certain value is known as a limit in mathematics.  
  • Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.
  • In addition to being closely related to limit and direct limit in category theory, the idea of a limit of a sequence is further generalized to include the idea of a limit of a topological net.

Solution -

[tex]f(x)=[x+4, x < -5[/tex] and [tex]4-x, x > 5][/tex]

[tex]lim_{x- > 5-(x+4)=-5+4} -1[/tex]

[tex]lim_{x- > 5+}(4-x)=(4-(-5))=9[/tex]

[tex]lim_{x- > 5-}[/tex] ≠ [tex]lim_{x- > 5+}[/tex]

Therefore, the limit does not exist.

Know more about the limits here:

https://brainly.com/question/23935467

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