Questions asked by Monzur R.

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• How can one prove that `ln(sec^2x+csc^2x) = ln(sec^2x)+ln(csc^2 x)`?
  
• Why isn't set-builder notation used for defining functions?
  
• Can I apply the sum-to-product formula to `cos3theta+(sqrt2-1)costheta` and how do I do it?
  
• How do I calculate the `"pH"` of the buffer solution when `1.00` `"g"` of potassium ethanoate is dissolved in `50.0` `"cm"^3` of `0.20` `"mol"` `"dm"^-3` ethanoic acid (`"K"_"a"=1.74xx10^-5` `"mol"` `"dm"^-3`)?
  
• How do I calculate the `"pH"` of the buffer solution formed when `10.0` `"cm"^3` of `0.80` `"mol"` `"dm"^-3` sodium hydroxide is mixed with `50.0` `"cm"^3` of `0.50` `"mol"` `"dm"^-3` ethanoic acid (`"K"_"a"=1.74xx10^-5` `"mol"` `"dm"^-3`)?
  
• The point `P(alpha,beta)` lies on the curve `C` with equation `f(x)= 1/3x+12/x` such that `alpha>0, alpha≠6`. The normal at `P` only crosses `C` once. How do I find the exact value of `alpha`?
  
• The angles in an `n`-sided polygon satisfy an arithmetic sequence with `a_1 =143^@` and `d=2`. Given that all of the internal angles of the polygon are less than `180^@`, how do I find `n`?
  
• How can I see which of my answers have been featured as great answers?
  
• When does an answer become 'yours'?
  
• Why does adding `"AgNO"_(3("aq"))` to `"I"_(2("s")) rightleftharpoons "I"_(2("aq"))` cause the aqueous iodine to precipitate into a solid?
  
• Why does `"NaOH"` only react with one acidic proton in salicylic acid even though both the carboxyl and the hydroxyl groups could potentially react with it?
  
• How did earlier mathematicians calculate limits so accurately?
  
• How do I solve `tan9x-tan2x=tan9xtan6xtan3x+tan6xtan4xtan2x`?
  
• Why is the line in bold valid (Picture added below)?
  
• Is there a way to stop receiving the 'Just asked' emails only?
  
• What is `d/dx(cosx(dy)/dz)` where `z=sinx`?
  
• Is it possible to find the following limit without using l'Hôpital's rule?
  
• How do we approximate `f^(-1)(x)`?
  
• How do I solve `648x+353y=1` for `x` and `y` working backwards from Euclid's algorithm for `gcd(648,353)`?
  
• How can I evaluate `lim_(x->0) (sinx-x)/x^3` without using L'Hopital's rule?
  
• Let `bbu`, `bbv`, `bb(w)` be vectors. How can we prove `bbu xx (bbv xx bb(w)) = (bbu * bb(w)) bbv - (bbu * bbv) bb(w)`?
  
• How do I evaluate `int_0^oo e^-x/sqrtxdx`?
  
• What is the maximum value of `Q(p,q,r)=2pq+2pr+2qr` subject to `p+q+r=1`?