Limits problem

  • Thread starter chukie
  • Start date
  • #1
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Solve:
lim x->0 (tan 3(x+h)-tan(3x))/h

i hv no clue where to start =(
 

Answers and Replies

  • #2
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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:
  • #3
Dick
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Did you mean lim h->0??
 
  • #4
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Did you mean lim h->0??
sry, yes i mean lim h->0
 
  • #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.
 
  • #6
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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)
 
  • #7
Dick
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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)
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.
 
  • #8
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kk thanks i got it =)
 

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