The whole concept of how limits worked took me a while to figure out mainly the part of discontinuity and continuity. I have trouble in trying to figure out whether a piecewise function is continuous or discontinuous.
One of the biggest problems I have is trying to figure out End behavior models for trigonometric functions without using a calculator for example problem number 38 on pg 95 which is f(x)=ln[abs(x)]+sinx. I was able to figure out the right end behavior model knowing that sinx was not really significant because the smallest value is -1 and that the biggest value is 1 so I knew that ln[abs(x)] was the right end behavior model.
I still have trouble in trying to figure out how to solve for horizontal asymptotes for a function. I am not sure whether there is a way to solve for it without having to graph it.
I was really confident about the limits test after seeing the practice test we got primarily because I did not see anything that gave me too much problem. After taking the test I was blindsided by a couple of problems on the test which is still bugging me that I was not able to solve which was one about explaining why a trigonometric function was continuous and to graph a sketch. The other one was the free response which had a piecewise function with a function having a variable on it.
Did you figure out the left hand behavior model for number 38? Those absolute value signs for the ln become really significant for that because that means that ln|x| is significant for negative inputs as well.
ReplyDeleteYou don't have to graph to find horizontal asymptotes. In fact, finding the horiz. asymptote first should help you to graph.