We'll talk about limits in class but I found an 8-minute video on Teacher Tube that I'd like you to watch. It's well-made and easy to understand.
Remember these three things:
- The word limit (or lim - the abbreviation) must be followed by a function.
- Beneath the word limit, you will find the part of the graph you're supposed to focus on. It will be described by an x-value.
- The answer to limit problems, if the limit exists, is always a y-value. It describes the intended destination of the function.
lim (x^3 + x - 1)
x---> 4
Evaluate this limit. What would happen to the limit if I restricted the domain to [-4, 4]?
Jake's function last week was y = sqrt(x)? Where, in its domain, does the limit not exist and why?
Have a good weekend... see you Tuesday.
- as x --> 4, lim--> 67.
ReplyDelete- when D: [-4,4] as X --> -4, lim --> -69, and
as X-->4, Lim --> 67.
- when X<0, no limit exists because you cant take a square root of a negative number
as x ---> 4, lim(x^3+x-1) = 67
ReplyDeleteD=[-4,4], as x ---> 4, lim(x^3+x-1) = DNE because x = 4 is an endpoint
if x<0 there is no limit because a square root of a negative number is undefined
As X approaches 4, the limit of the "x^3+x-1" function will approach 67.
ReplyDeleteIf the domain was restricted to [-4,4], I think it'd only restrict the values of the answers being between -69 and 67, including those numbers if they were to actually touch the limit.
No limit would exist for any values squared less than 0 because it'd cause the numbers to be imaginary, and we aren't dealing with those, so it wouldn't exist...
-Michael Ferrer
When x--> 4 lim (x^3 + x - 1) is 67.
ReplyDeleteWhen the domain is restricted [-4,4], x--> -4 lim--> -69 and x--> 4 lim--> 67.
For Jake's function, y=sqrt(x), there cannot be a limit because x cannot be less than 0 because you would end up with imaginary numbers and undefined answers.
Jake, I will call on you to explain your first answer above - it was spot on! Regarding y = sqrt(x), you all are close. I asked you to consider only the points that are in the domain. Of course, 0 is in the domain but the limit does not exist at 0. Reread Jake's comment about the other function and see if it makes sense.
ReplyDelete1. lim x^3+x-1 = 67
ReplyDeletex--> 4
2. when D=[-4,4], for x --> -4 lim --> -69 and for x --> 4, lim --> 67
3. If y = sqrt(x), any negative number would have an imaginary limit
-Jacob Stein