Sorry for the delay, but better late then never
So Limits is what is the hardest for me so far, theres just some things that confuse me
1. What really confuses me about limits is using them to find the continuity, discontinuity and points of conitnuity. I also dont really understand if their is limit of infinity or if there is NO limit at all, i dont know what is the difference between them.
2. I also have troubles finding the limit as it aproachest infinity and negative infinity without a graph. With graphs i can pretty much find it but without them i have trouble if the equation is very large.
3. Limits are also confusing when using them to find the slope of tangent and secant, im confused whether we have to find the limit as f(x) approahes 0 or as it approaches a certain constant.
Definitely better late than never.
ReplyDelete1. If you CAN plug the numbers in, it is continuous for those points (except for int x). If you CANNOT plug the numbers in, it is NOT continuous.
There is a difference between having a limit that goes to infinity and having no limit. Something like sin x or cos x alone would have no limit as x-->infinity because it keeps oscillating back and forth between 1 and -1. something like y=2x would be infinity because as x grows indefinitely, so does the output.
2. Limits to infinity, you always want to simplify to it's end-behavior model. After all, we're looking to see what happens all the way out at the ENDS.