Question

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

Answer 1

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,

$\lim_{x \to -2} f(x)$

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

• The second function is given as,

$\lim_{x \to 0} f(x)$

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,

$\lim_{x \to 2} f(x)$

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,

$f(2)$

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,

$\lim_{x \to 4} f(x)$

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,

$\lim_{x \to \infty} f(x)$

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