DarkAngelBGE Posted March 16, 2004 Share Posted March 16, 2004 Okay, it's late, but I started with the question of f'(ln x):f'(ln x) = lim(h -> 0) ( [f(x0 + h) - f(x0)] /h )= lim(h -> 0) ( [ln(x0 + h) - ln(x0)] /h )= lim(h -> 0) ( ln( [x0 + h] / x0) /h )Will have a closer look later. Gotta revise some log rules. Indeed ln x is logarithmus naturalis == log of x, base being e. Link to comment Share on other sites More sharing options...
akya Posted March 16, 2004 Share Posted March 16, 2004 euh...what was the problem again ?f'(ln x) = 1/xf''(lnx) = -1/(x^2)f'''(lnx) = 1/(x^3)etc.f(x,y)=x^2 + 4xy + sin y +y^2what are the derivatives f'x and f'y ?[edit] not a simple question I'll find another one Link to comment Share on other sites More sharing options...
Curufinwe Posted March 17, 2004 Share Posted March 17, 2004 Curu, you sure you didn't want to ask: (x-4)(x+4) ? Well, not really ... I just wanted those who answer to be a little confused ... you always have (x-4)(x+4) in class ... just wanted to make it a little different Link to comment Share on other sites More sharing options...
King Tutankhamun Posted March 17, 2004 Share Posted March 17, 2004 Would that be if you used FOIL be x^2 - 16 ? Link to comment Share on other sites More sharing options...
Jeru Posted March 17, 2004 Share Posted March 17, 2004 (4-x)(x+4) = (4-x)(4+x) = 4^2 - x^2 = 16 - x^2A little problem of my own:f(x) = e^2xf'(x) = ?(...and I'll use the opprotunity for a shout-out to Smadar, the best math teacher I've ever met!) Link to comment Share on other sites More sharing options...
chichigrande Posted March 17, 2004 Share Posted March 17, 2004 (4-x)(x+4) = 4x+16-x^2-4x=16-x^2Ok here's one: simplify the problem: 2x^2+13x+9 Link to comment Share on other sites More sharing options...
CodeOptimist Posted March 18, 2004 Author Share Posted March 18, 2004 Ok here's one: simplify the problem: 2x^2+13x+9 Can that be simplified?Edit: Is that 2x^2? or (2x)^2?(boy, I wish you could do sub/super-script ) Link to comment Share on other sites More sharing options...
Dnas Posted March 18, 2004 Share Posted March 18, 2004 Well...If you mean (2x)^2..Then it would be (4x+9)(x+1). Link to comment Share on other sites More sharing options...
CodeOptimist Posted March 18, 2004 Author Share Posted March 18, 2004 Matt? Did Dnas get it right? Link to comment Share on other sites More sharing options...
King Tutankhamun Posted March 18, 2004 Share Posted March 18, 2004 I am thinking that Matt wants the Quadratic formula used. -b+- |b^2-4ac_____________ 2aor you could do factoring. (2x+ ?)(x+ ?)Wait a min Matt did you just make that one up because I went thorugh it and it won't work properly. Do you mean 9x-13? Link to comment Share on other sites More sharing options...
Dnas Posted March 19, 2004 Share Posted March 19, 2004 2(x^2)+9x-13 can't be factored either.It's discriminant isn't a square number. Link to comment Share on other sites More sharing options...
chichigrande Posted March 19, 2004 Share Posted March 19, 2004 No, I had it right. Desmond was the closest with demonstarting the quadratic formula.Here's how it would be:2x^2+13x+9 -> (-13+-l169-72)/4 [(-b+-lb^2-4ac)/2a] -> (-13+-l97)/4-> (-13+9.88)/4 or (-13-9.88)/4 -> x=-0.78 and -5.72 Link to comment Share on other sites More sharing options...
akya Posted March 19, 2004 Share Posted March 19, 2004 anyone want to try out my problem (I posted a while ago) ? Couldn't find an easier one... ... I'll keep searching Link to comment Share on other sites More sharing options...
King Tutankhamun Posted March 19, 2004 Share Posted March 19, 2004 Hey Matt, I got those answers when I worked them out but thought they were odd and therefore thought I made a mistake.I guess I will ask one:What is the ratio of short leg:long leg:hyp in a 45,45,90 triangle? Link to comment Share on other sites More sharing options...
MarkT Posted March 19, 2004 Share Posted March 19, 2004 Akya - Oh well, if nobody else is going to guess:f(x,y) = x^2 + 4xy + sin y + y^2(df/dx)y = 2x + 4y(df/dy)x = 4x + cos y + 2y Link to comment Share on other sites More sharing options...
Dnas Posted March 19, 2004 Share Posted March 19, 2004 What is the ratio of short leg:long leg:hyp in a 45,45,90 triangle? Easy.1:1:sqrt(2)ORsqrt(2):sqrt(2):2(I don't know if simplest radical form is needed here.) Link to comment Share on other sites More sharing options...
King Tutankhamun Posted March 19, 2004 Share Posted March 19, 2004 Dnas you gots it right. Link to comment Share on other sites More sharing options...
CodeOptimist Posted March 19, 2004 Author Share Posted March 19, 2004 Good job! ;) Link to comment Share on other sites More sharing options...
Dnas Posted March 19, 2004 Share Posted March 19, 2004 What do you define as a "simple" problem?A polynomial of degree 4, in the form x^4+ax^3+bx^2+cx+d=0 (a,b, and c are all real numbers), has roots -4+3i and 9+4i. What is the value of a?(I wonder how many 7th graders can solve this.) Link to comment Share on other sites More sharing options...
CodeOptimist Posted March 19, 2004 Author Share Posted March 19, 2004 I guess "simple" would be defined as up through Pre-Algebra/Algebra... let's skip Algebra II Link to comment Share on other sites More sharing options...
Tonto_Icy_Tripod Posted March 19, 2004 Share Posted March 19, 2004 This is why having different maths systems sucks. I've got no idea what you do in algebra... logs? functions? Trig? (um, prolly not) Link to comment Share on other sites More sharing options...
CodeOptimist Posted March 19, 2004 Author Share Posted March 19, 2004 Well basic Algebra is ratios, solving for variables, etc. Functions are in there, I think logs are later on in Algebra II. Definetly not trig Link to comment Share on other sites More sharing options...
Dnas Posted March 19, 2004 Share Posted March 19, 2004 Okay. How about this one?Factor x^4+x^2+1It is Algebra I.Well... Sort of. It's a combination of really basic math, algebra (1), then more algebra (1). Link to comment Share on other sites More sharing options...
King Tutankhamun Posted March 19, 2004 Share Posted March 19, 2004 I know it, but I will let someone else give it a shot.I think in here we start to use trig in geometry a little bit. Link to comment Share on other sites More sharing options...
last samurai Posted March 20, 2004 Share Posted March 20, 2004 (x^2+x+1)(x^2-x+1) Link to comment Share on other sites More sharing options...
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