So far, the lectures have been comprehensible, and the material feels strangely intuitive. I’ve been mostly in the math zone with homework, getting most problems right right away. However, I am perplexed by the fact that, as I ascend into higher, more abstract math, I get derailed by the basics.
For example — just a week or so ago, I was befuddled by the simplest absolute value problems. This week, I suddenly forgot how to add. I also often overlook negative signs, which changes the answer completely.
Thankfully, we have moved past decimals. Goodness knows what horrors I would wreak by placing that tiny dot in the wrong place!
That is not to say, of course, that I am mastering all of the new material. We had several sandwich theorem problems on the homework, and I came across one that was downright indigestible (sorry, I’m not allowed to pun much in my professional writing, so I have to get it out here).
I wasn’t the only one having trouble, which is gratifying, but the Calc Professor wouldn’t help me or anyone else solve it when we asked. He told me to think about it some more. I have! He told me to come to office hours Wednesday before the test. I will!
The issue is that in the meantime, this problem is starting to affect me in much the way a grilled panino did four years ago. Said panino was so hard I broke a molar on it. I had to get a crown, which cost me $500 even with dental insurance. I am NOT fond of that panino.
So … kind mathematicians who read this blog, I need your help. What the heck do I do with the problem below?
|x|/square root of x^4 + x^2 + 4
With some hints and a lot of sweat, I came up with this:
0 < |x|/square root of x^4 + x^2 + 4 < |x|
Fantastic! Now what? Should I do some algebra magic on the function in the middle? Say take the absolute value off x, and rationalize the denominator?
The equation should then look like this:
x (square root x^4 + x^2 + 4) / x^4 + x^2 + 4
I am stuck there. I am not even sure all of the above was necessary.
Ugh. I can feel my molar aching. And I just know calc professor is going to have something equally evil on the test. Maybe the other problems won’t be so bad?
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