Worth saying plainly since you are new: this only works if the balance is paid in full every month, automatically. Interest at typical card rates wipes out any bonus you are chasing within a couple of months. If there is ever a month where that is uncertain, skip the card.
Abigail Ruthven
@abigail_ruthven
Recruiter on the agency side, now in-house. I read roughly four hundred resumes a month and I promise most rejections are boring, not personal.
Your classmates who finished in twenty minutes had either seen a near identical proof before or they wrote something that will not survive marking. Both are extremely common. Do not calibrate on other people's self reports.
It is not a wasted two months, you just measured a channel and learned it is not your channel. That is a real result.
The loop is the method, not a mistake. Name the whole thing: let I = ∫ e^x sin(x) dx. After two rounds of parts you end up with something like I = e^x sin(x) - e^x cos(x) - I. That is an equation, so add I to both sides and divide by 2, and you are done.
The one thing that will break it: you have to differentiate the same kind of function both times. If you differentiate the trig on round one and then differentiate the exponential on round two, you undo your own work and everything collapses to 0 = 0.
Targeted algebra review, not a whole precalc course. Six weeks at 45 minutes is about 30 hours, which is nowhere near a full precalc sequence but is plenty for a triage list.
The things that actually sink people in Calc 1, in the order they will hurt you:
- factoring and simplifying rational expressions, because every limit problem is this in disguise
- exponent and log rules, both directions
- the unit circle and the values of sin and cos at the standard angles, cold
- function notation and composition, especially
f(g(x))for chain rule later - graph transformations, shifts and stretches
If you can do those five without hesitating, you are ready. Skip conic sections, skip matrices, skip most of the trig identity zoo.
It is common in their industry apparently, which now makes me wonder whether I have been selling to the wrong industry all along.
The CSV question is a good one, I jumped straight to how rather than why. Asking tomorrow.