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Limits problem

  1. Jun 9, 2008 #1
    Solve:
    lim x->0 (tan 3(x+h)-tan(3x))/h

    i hv no clue where to start =(
     
  2. jcsd
  3. Jun 9, 2008 #2
    err.. tan (3h)/h?

    simply plugging in 0 for x..

    edit: are you sure x is approaching 0?

    initially, I thought it's h..

    then the answer would have been 3+3tan(3x)^2
    and you had to do some mess with identites..
    http://www.clarku.edu/~djoyce/trig/identities.html
     
    Last edited: Jun 9, 2008
  4. Jun 9, 2008 #3

    Dick

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    Did you mean lim h->0??
     
  5. Jun 9, 2008 #4
    sry, yes i mean lim h->0
     
  6. Jun 9, 2008 #5

    Dick

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    Look up a formula for tan(A+B) and apply it to tan(3x+3h). Then simplify, take your limit and use some trig.
     
  7. Jun 9, 2008 #6
    It is actually very simple.. don't even need to any trig after simplifying tan(3x+3h) ..

    should factor out things.. and they would cancel out nicely.

    And, one more thing tan(x)/x = 1 .. (which is simple to prove is you know sin(x)/x =1 as x-->0)
     
  8. Jun 9, 2008 #7

    Dick

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    Yep. You don't have to use any trig. But using sec^2(A)=1+tan^2(A) would put it in the simpler form listed in books.
     
  9. Jun 10, 2008 #8
    kk thanks i got it =)
     
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