-Max Chellemi
Here is the Question of the day!
True or false...sorry Rachel ; ) hehe
The function f(x) = cos(x) - sin(x) is increasing in
Lets analyze the question. We need to be able to visualize the graphs of sin(x) and cos(x). We also need to know that we are looking to see that the value of the output {f(x)} is increasing in value between the given parameters. Remember when the function is said to be increasing there may be no decreasing values in the output of the function between the given parameters.
Ok we know that the graph of sin(x) looks like
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We also know that the graph of cos(x) looks like
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Ok sorry for the layout issues but you don't know how hard this is...or how slow i am haha but i am trying. Ok so now that we have the graphs we can start tho think about this.
alright. We don't care about any part of the function that has an x less than zero or greater than π/2. We observe that the two functions cross at pi/4 and are the farthest apart as we approach π/2.
Graphically we can already see that the function doesn't increase the entire time but now we must examine it numerically to solidify our argument. Lets pick two easily identifiable points and check our hypothesis with a table.
| x | f(x) = cos(x) - sin(x) |
| 0 | 1 |
| π/4 | 0 |
We need go no further ladies. As clearly indicated in the table above we increased the "x" value and the "y" value decreased, ergo the function is not solely increasing between
Today’s lesson talked about the Corollary to the Theorems that we received yesterday concerning continuity (the three things). The theorem reads: suppose “g” is continuous at “a” and “f” is continuous at g(a), then the function is continuous.
I hope this was helpful for you guys! Get well! I mean it!
Night
-Max Chellemi
3 comments:
max, thank you so much! you are my hero!!!!
Max,
Excellent! Excellent! Excellent!
You have set a high standard for the following acts.
Feel free to share any tricks that you learned in creating this post. That sounds like a post of its own.
Again, thank you for moving us forward.
Thank you so much Max. This is spectacular!
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