Question

Limits and Continuity??

Answer 1

what are \[\lim_{x \rightarrow \infty} \] and \[\lim_{x \rightarrow -\infty} \] of

Answer 2

I believe it should be as a coordinate point so
limit approaching infinity: [2,infinity)
limit approaching -infinity: (-infinity, -2]

Answer 3

so you have x=2 and x=-2

Answer 4

okay. How bout
For the following graph, what is \[\lim_{x \rightarrow \infty}F(x)\]

Answer 5

Are you looking for horizontal or vertical asymptote?
I am thinking it is horizontal so lim as x approaches infinity is 0

Answer 6

Whenever you have a graph look at the graph and determine if they want the vertical or horizontal asymptote. So you can get the limit of the function as x approaches infinity

Answer 7

What is \[\lim_{x \rightarrow \frac{ \pi }{ 2 }}f(x)\]

Answer 8

I'm not sure about this one but i think the limit should be 1

Answer 9

oops i forgot the options.
0
-infinity
infinity
DNE (Does Not Exist)

Answer 10

For your very first question (and you really should make each question a new post), it looks like as x-> infinity, the graph is approaching the x-axis. i.e. y->0
the limit is 0

Answer 11

For the last question, what is y when x= 0.5 pi ?

Answer 12

infinity?

Answer 13

yes

Answer 14

What is \[\lim_{x \rightarrow 3} f(x) \]

Answer 15

DNE?

Answer 16

It is a one-sided limit (either + infinity or - infinity)
but x->3 means if we approach 3 for either side, we get the same limit.
Here we do not, so the two-sided limit does not exist.

Answer 17

Explain why Sin1/x is not continuous at x = 0.

Answer 18

when x is small, example x= 0.01
1/x is big 1/0.01 = 100

sin(100 radians) is some number between -1 and +1. As if we make x smaller, 100 gets bigger, and the new sin value will bounce around between -1 and +1. There is no number that the sin(1/x) is approaching as x-> 0.

Answer 19

Describe a case where f(x) has a limit but is not continuous.

Answer 20

see https://www.khanacademy.org/math/calculus/limits_topic/limits_tutorial/v/introduction-to-limits--hd

Answer 21

..... it said an error occured please try again later

Answer 22

Here is the same thing, but on Youtube
https://www.youtube.com/watch?v=riXcZT2ICjA#t=343

Answer 23

show using limits that f(x)=tan(x) is continuous at x=0