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let me upload the pic jst a sec
Both 2 and 3 i dont understand
regarding 2, I dont understand what it means by pi/2^+
same thing with pi/2^-
|dw:1442798477466:dw| If you look up any tangent graph, you will see that it approaches +inf at x just below pi/2, and approaches -inf at x just above pi/2. These are the respective limits of tan(x) at x=pi/2- and pi/2+. The definition of a limit if it exists, is that if lim x->pi/2- of tan(x) \(equals\) lim x->pi/2+ of tan(x), than lim x->pi/2 of tan(x) = the value of the limits. If limx->pi/2+ does not equal to lim x->pi/2-, then the limit does not exist.
so the negative and the positive sign are letting me know that?....
pi/2- means approaching from the left, or a value slightly below pi/2. Look at the graph, at a point just on the left of pi/2, the function tends to +inf. Pi/2+ means approaching from the right, or a value slightly above pi/2. The graph shows that immediately to the right of pi/2, the function tends to -inf. To do limits involving vertical asymptotes, it would be good to develop a habit and ability to draw a graph of the given function, as I have done for you. This way, the limits will be clear.
I am still not understanding
So the negative and positive only let me know which side x is approaching
I have this already graphed on my ti 84 so i see the graph
Still need help guys
How does the +/- affect the equation?
The +/- does not affect the equation or the graph, but it affects 1. whether the limit exists at a point x=c 2. what is the limit of the function at x=c,....if the limit exists. For example, if the left limit (i.e. limit x->c- ) equals +inf, and the right limit (i.e. limit x->c+ ) equal -inf. What can you say about the limit at x=c? Is it +inf, or -inf? Since we cannot answer the question logically, we say that the limit at x=c does NOT exist. On the other hand, if both "one-sided limits" have the same value, say +inf, then we say that the limit x=c exists, and equal to +inf.