Limit of f(x) as x approaches 1, if the limit exists

[Math-hating-Aggie]

Find the value of f(x) as x tends toward 1, when:

. . . . .. ./ 6x − 1, x not equal to 1
f(x) = <
. . . . .. .\ 8, x = 1,

...if the limit exists.

1. limit = 4
2. limit = 5
3. limit = 8
4. limit = 6
5. limit does not exist
6. limit = 7

 

[stapel]

If you're not sure of the limit, then try graphing the function. The limit should be immediately obvious. :wink:

Eliz.

 

[Math-hating-Aggie]

I still can't get it

 

[stapel]

I still can't get it

What does your graph look like? What is it doing, right around x = 1?

Please be specific. Thank you.

Eliz.

 

[Math-hating-Aggie]

What does your graph look like? What is it doing, right around x = 1?

It looks really odd. I am not that much of a math person so I think there's a problem. I think the Limit doesn't exist but I am not sure

 

[stapel]

It looks really odd.

Please clarify what you mean by this. (Since the graph should be a simple straight line, with one dot off to the side, similar to some of the rational functions you graphed back in algebra, we'll need a clear description and/or a link to a graphic, in order to "see" what it is that you're doing instead.)

Thank you.

Eliz.

 

[soroban]

Hello, Aggie!

Find the value of: \(\displaystyle \L\,\lim_{x\to1}f(x)\) when:

. . \(\displaystyle f(x)\:=\:\left\{\begin{array}{cc} 6x\,-\,1 & \;x\,\neq\,1 \\ 8 & \;x\,=\,1\end{array}\)

\(\displaystyle (1)\;4\;\;\;(2)\;5\;\;\;(3)\;8\;\;\;(4)\;6\;\;\;(5)\text{ does not exist}\;\;\;(6)\;7\)

Did you graph it correctly?

\(\displaystyle y\:=\:6x\,-\,1\) is a straight line . . . how hard is that?

The graph looks like this:

        |                   *
       8|       *         *
        |               *
        |             *
        |           *
        |         *
        |       o
        |     *
      --+---*---+--------------
        | *     1
        *
      * |
    *   |

The graph is the line \(\displaystyle y \:=\:6x\,-\,1\)
. . except when \(\displaystyle x\,=\,1\), we are told that \(\displaystyle y\,=\,8.\)

So we have a line with a "hole" at \(\displaystyle (1,5)\)


Now, do you understand enough about limits to answer the question?

 

[Math-hating-Aggie]

I did not draw the graph..........I meant the question looked odd

 

[stapel]

I did not draw the graph.

Why not? Or were you just waiting to be given the answer...?

Eliz.