1. An example of one that I had no clue how to do was #5 on the test. The problem was finding the limit as x approaches negative infinity of f(x)= cos 3x/x.
2. Another example of a limit problem that I had trouble with was #7 on the test. I was pretty confident about the answer I had gotten for it, until I got my test back. The problem was finding the limit as x approaches pi/2 from the positive side of f(x)= tan x.
3. Another problem that was unfortunately also on the test was was the one where we had to find the limit as x approaches -2 of f(x)= 1/x+2
For #5, remember that as x approaches infinity of cos3x/x, the graph is slowly moving closer to 0, therefore your answer would be 0.
ReplyDeletefor #6, I graphed 1/x and moved it 2 units to the left, and since as x approaches -2 there is an asymptote and on the right of that asymptote the line approaches infinity and on the left of the asymptote it approaches negative infinity, then the limit does not exisit because there cannot be 2 different values for the limit as it approaches -2. In contrast, if it would have said either from the positive side or from the negative side, then the limit would have existed. but since it is asking for -2 in general, the limit must be equal coming from both the positive side AND the negative side (left and right).
For #7, You just have to remember what the graph of tangent looks like. the asymptotes would be pi/2, 3pi/2, etc. So if you just imagine the graph approaching from the positive side, you realize that the line goes downwards towards NEGATIVE INFINITY.
I hope this helps, and P.S., dont draw the tangent graph backwards like I did hahaha!
=) I have your response on an index card.
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