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Given the piecewise function above evaluate the following statements. (write "DNE" if the limit does not exist)

Given The Piecewise Function Above Evaluate The Following Statements Write DNE If The Limit Does Not Exist class=

Sagot :

The piecewise function of the above evaluate the following statements has the limit of the function as,

  • a) Does not exist (DNE)
  • b) 3
  • -1
  • 3
  • e) Does not exist (DNE)
  • 2

What is the limit of a function?

The limit of a function at a certain point is the points, or boundary, in which the function can be existed.

  • The first function is given as,

[tex]\lim_{x \to -2} f(x)[/tex]

Here, the limit of the function is -2. This limit does not exist for the given graphed function.

  • The second function is given as,

[tex]\lim_{x \to 0} f(x)[/tex]

Here, the limit of the function is 0. At this limit the function is continues and the value of the function at point 0 is 3.

  • The third function is given as,

[tex]\lim_{x \to 2} f(x)[/tex]

Here, the limit of the function is 2. At both the place, upside or downside, we get the value as -1. Thus, the value of function is -1.

  • The forth function is given as,

[tex]f(2)[/tex]

Here, the function has the initial value 2. At this value, the value of the function is 3. Thus, the limit of the function at this point is 3.

  • The fifth function is given as,

[tex]\lim_{x \to 4} f(x)[/tex]

Here, the limit of the function is 4. For this limit, the asymptotes goes from positive infinite and negative infinite. Thus, the limit does not exist for this point.

  • The sixth function is given as,

[tex]\lim_{x \to \infty} f(x)[/tex]

Here, the limit of the function is ∞. For this limit, the function will tend asymptotically to the number 2.

The piecewise function of the above evaluate the following statements has the limit of the function as,

  • a) Does not exist (DNE)
  • b) 3
  • -1
  • 3
  • e) Does not exist (DNE)
  • 2

Learn more about the limit of a function here:

https://brainly.com/question/23935467

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