Graphing Real Functions: Limits at Infinity and Complex Numbers Explained

[Jadenag]

We have to graph these functions where they are real. (no need to graph where complex)

d)
For d I am getting a point at (1,0) and then half a c shaped graph opening towards the right. Is
this correct?
g)
For g I have 0 on the negative side. and a straight line in the first quadrant. :s I am not sure about this one.

I have to find the limit.
I realize this has two different directional limits positive and negative infinity. does that mean the actual limit does not exist?

Is this very easy? I mean iim confused do i simply have to plug in underroot etc or is it something much more complicated :S

 

[HallsofIvy]

We have to graph these functions where they are real. (no need to graph where complex)

d)
For d I am getting a point at (1,0) and then half a c shaped graph opening towards the right. Is
this correct?

Half correct. What about t<1?

g)
For g I have 0 on the negative side. and a straight line in the first quadrant. :s I am not sure about this one.

No, that is not correct. You should have a "stair step". If x is between 0 and 1, n= 0 so the value of the function is 0. For x between 1 and 2, n= 1 so the value of the function is 1. If x is between 2 and 3, n= 2 so the value of the function is 2, etc.\

I have to find the limit.
I realize this has two different directional limits positive and negative infinity. does that mean the actual limit does not exist?

Yes, any time you have a fraction where the denominator goes to 0 and the numerator does not, the limit does not exist.

Is this very easy? I mean iim confused do i simply have to plug in underroot etc or is it something much more complicated :S

It looks to me like there is a serious typographical error in this problem! The point of the exercise is to show that, as x gets closer and closer to 2, f(x) gets closer and closer to 4 and then show that you can use the same argument with the general \epsilon as you did with .01 and .001.

(a) asks "What is the value of x_1 such that f(x)= 2+ 0.01". That obviously should be "f(x)= 4+ 0.01"! And (b) should be " "What is the value of x_1 such that f(x)= 4- 0.01". f(x)= 4+ 0.01 is the same as x^2= 4.01. Find x_1 by taking the square root of both sides.