Why are you plugging in 0?If I'm approaching 1 from the left, then that means I should be able to plug 0 into the function. So why does 0 not work but 1 does?
The limit asked me to approach from the left of 1. Left of 1 is zero....
It also states that x can be <= to 1. Therefore any number less than 1 should be a number that I could plug in. So I chose 0 and it failed. If thats the case then the limit is NOT a number <= to 1. Its just 1.
The notation \(\mathop {\lim }\limits_{x \to \bf{1^ - }} \) means that \(x\) is close to \(1\) on the left (the negative) side.It also states that x can be <= to 1. Therefore any number less than 1 should be a number that I could plug in. So I chose 0 and it failed. If thats the case then the limit is NOT a number <= to 1. Its just 1.
Presumably you are learning about what limits mean, and specifically what "approach from the left" means; that's what you need to figure out.Hmmm...I guess I gotta keep tinkering with it.
I got all of the answers right. Just a little confused on the wording.
Sounds like your talking about Epsilon and Delta. As a point gets approached on x then the other point moves along y.... Correct?Presumably you are learning about what limits mean, and specifically what "approach from the left" means; that's what you need to figure out.
Have you tried discovering what it means by doing the things we've suggested? One is to draw the graph, and see what happens to y as you move a point along it toward x=1. Another is to calculate values of y for values of x like 0, .5, .9, .99, ... approaching 1 from the left.
In both cases, the limit they are asking for is the number that y approaches as you do these things; what you'll discover is that, because this function is continuous to the left of x=1, that limit is exactly what you get when you plug in x=1.
What you need to see is why that is true, and how you can know it for yourself without having to ask.
What part of the wording still confuses you?
I wasn't explicitly referring to epsilon and delta, just to the informal idea of a limit. And I want you mostly to think informally. Again, have you done any of the things we suggested, which are meant to help you do that?Sounds like your talking about Epsilon and Delta. As a point gets approached on x then the other point moves along y.... Correct?
Im taking calculus 1 class over the summer. Im only 4 days in and we move extremely fast. Some of the things you say havn't completely clicked yet..I'm getting there though...I wasn't explicitly referring to epsilon and delta, just to the informal idea of a limit. And I want you mostly to think informally. Again, have you done any of the things we suggested, which are meant to help you do that?
But, yes, as you change x, y = f(x) also changes, so the point (x,y) moves along the graph.
The question is, do you see yet why in your problem, as x approaches 1 from the left, y will approach f(1) = 14?
And then, do you see what this is not true as you approach from the right?
Here's the graph:
View attachment 27648