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What is the end all definition of a catalyst? Conc acids are used to speed up the rate of reaction/lower activation energy/increase rate of reaction both ways in equilibrium, but surely if conc acids are dehydrating agents then they are actually getting involved in the equlibrium, e.g. favouring...

general solution of cos4x + cos2x = sqrt2 . cos^2(x) + 1/sqrt2 . sin2x

hey ive seen a few questions that use different definitions of the tk+1 term to get the greatest coefficient the way i was shown u define the tk+1 as nCk and then tk as nCk-1 and then have tk+1/tk >= 1 its a bit weird though cos in the trial there was a question to prove this, and i...

By taking cylindrical shells find the volume enclosed in the region enclosed by (x-1)^2 + y^2 = 1 I ended up getting like the integral of x(2x-x^2)^1/2 I couldn't get it. Is my integration shice or is there a trick to these kinds of questions, like 2 semi-circles or something. if...

integ x secx tanx dx I got: x secx - ln|tan(45 + x/2)| + C 45 being in degrees I'm pretty sure it's right, but am not sure how the book got x secx - ln(secx + tanx) + C Is my answer wrong? How did they get theres? Thanks