Question

Evaluate each limit. this is in the topic of jump discontinuities.

Answer 1

To evaluate limits for jump discontinuities, follow a step-by-step process: identify the point of discontinuity, find the left-hand and right-hand limits, and determine if they are equal.

Step-by-step explanation:

In the context of jump discontinuities, evaluating limits involves finding the value that a function approaches as the input approaches a certain point.

Here's a step-by-step process to evaluate limits for jump discontinuities:

1. Identify the point at which the jump discontinuity occurs.
2. Take the limit of the function as the input approaches the point from the left side.
3. Take the limit of the function as the input approaches the point from the right side.
4. If the left-hand limit and right-hand limit exist and are equal, then the overall limit exists and is equal to the common value.
5. If the left-hand limit and right-hand limit do not exist or are not equal, then the overall limit does not exist.

Answer 2

we have

`\begin{gathered} \lim _(x\to-2)-x^2-4x-5 \\ \lim _(x\to-2)-(-2)^2-4(-2)-5 \\ \lim _(x\to-2)-4^{}+8-5 \\ \lim _(x\to-2)--1 \end{gathered}`
`\lim _(x\to-2)-1=-1`

therefore

the answer is -1