solutions to the pretest

let me know if you find any errors. no solutions for the proofs, though.

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Tags: calculus, differentiation, integration, test

This entry was posted on May 9, 2009 at 3:27 am and is filed under math. You can follow any responses to this entry through the RSS 2.0 feed.
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May 10, 2009 at 10:37 am

I would argue that your answer to Problem 8 is incorrect, but it is more a matter of bad notation. Mixing dummy variables of integration and limit variables is prone to error. If you are going to mix them, I would say

int _0 ^{x^2} 2x dx = x^4 with derivative 4x^3

which in the notation of the Problem is 2xf(x^2) but there is no sign of the other term.

May 10, 2009 at 11:53 am

Hi Kiwi,

I understand your objection. My thinking was to treat is as a purely formal problem where the variable in the integrand is the same variable as in the limit of integration. But now that you point it out, that doesn’t make any sense. I’ll change the problem to something more reasonable. Thanks for pointing this out!