Discovering Limits: Solving for x Approaching Zero from the Left

[ashleyk]

I need some help on my take home AP test. We have been taking the limit as the function approaches infinity but this is problem is when the limit approaches zero from the left...so I'm not sure if I can do that same steps.

Find the limit.

(limit as x approaches zero from the left) (1 + (1/x))


Any help would be great...

 

[arildno]

Well, what is your gut feeling about the expression when x runs through the negative numbers up to 0 ?

 

[Jameson]

Test points extremely close to zero from the left and see what trend they have.

-.1 , -.01 , -.000001

 

[HallsofIvy]

Or, if you feel more familiar with limits at infinity, let y= 1/x and look at 1+ y.

As x-> 0, what happens to y? what happens to 1+ y?

 

[marlon]

(limit as x approaches zero from the left) (1 + (1/x))


Any help would be great...

Well let's look at 1/x...just as in any fraction, you know that if you divide a number (here 1) by something real small you get something real big. So what do you think 1/0 will have as solution...it is going to be real big.

The second part will be to determin whether this "real big thing" is positive or negative. You can check this by making a sign chart of the function
$$\frac{x + 1}{x}$$ which is the same function that you gave, only written in a more convenient way to make sign charts. Just look at the numerator and the denominator apart. Can you make the sign chart of a function like ax +b ?

marlon