Limits

[Aveym]

Hi there! Our teacher started a new lesson today which she didn’t really teach properly as the concept is still fairly hazy to me. Could someone please help me with the following? Essentially how to go about the “x= -4” part. Do they need me to plug in the no. In f(x) ? Any help would be appreciated. Thankyou!

 

[Steven G]

These are great questions but we want to see your answers with explanations. On this forum we do not solve any problems for students. We prefer that the student solves their problem with hints from the forum helpers.

Did you draw a graph that has those given properties? Please post it.
Do you know the definition of a function to be continuous at a point? Please state it.

 

[Aveym]

Yes I understand, I would definitely solve them on my own i just need a direction as i dont know where to start from. Although, i do know for a for a function to be continuous at a value of X= a, the following three conditions are to be satisfied: 1. F(a) is defined. 2. The limit of f(x) as x approaches a exists. 3. Limit of f(x) as x approaches a is equal to f(a).

 

[Steven G]

Fine, but you need to tell us where you are stuck.
You have the correct definition for a function to be continuous at a point. So what seems to be the problem using it. Please tell us.
Can you draw any function that satisfies the given information? Once we have the graph things will move quickly.

 

[pka]

The first sentence reads: "Is each statement is true or false?" Well yes, that is the very definition of a mathematical statement in logic.