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Limits problem

by chukie
Tags: limits
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chukie
#1
Jun9-08, 10:08 PM
P: 82
Solve:
lim x->0 (tan 3(x+h)-tan(3x))/h

i hv no clue where to start =(
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rootX
#2
Jun9-08, 10:14 PM
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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
Dick
#3
Jun9-08, 10:16 PM
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Did you mean lim h->0??

chukie
#4
Jun9-08, 10:17 PM
P: 82
Limits problem

Quote Quote by Dick View Post
Did you mean lim h->0??
sry, yes i mean lim h->0
Dick
#5
Jun9-08, 10:26 PM
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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.
rootX
#6
Jun9-08, 10:41 PM
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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)
Dick
#7
Jun9-08, 10:45 PM
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Quote Quote by rootX View Post
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.
chukie
#8
Jun10-08, 12:58 AM
P: 82
kk thanks i got it =)


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