Limit problem

  • Thread starter terryds
  • Start date
  • #1
392
13

Homework Statement



##\lim_{a\rightarrow b} \frac{tan\ a - tan\ b}{1+(1-\frac{a}{b})\ tan\ a\ tan\ b - \frac{a}{b}}## = ...


Homework Equations



tan (a - b) = (tan a - tan b)/(1+tan a tan b)

The Attempt at a Solution


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I don't know how to convert it to the form of tan (a-b) since there are some extras in the denominator
Please help
 

Answers and Replies

  • #2
member 587159
Use distributivity in the denominator and then factor it .
 
  • #3
robphy
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Looking only at the denominator, can you write it in another way?
 
  • #4
392
13
Use distributivity in the denominator and then factor it .
Looking only at the denominator, can you write it in another way?

Alright, I've just noticed it...

##lim_{a->b}\frac{tan\ a - tan\ b}{(1-\frac{a}{b})(1+tan\ a\ tan\ b)} = lim_{a->b}\frac{tan (a-b)}{(\frac{b-a}{b})} = -b##

Thanks for help!
 
  • #5
member 587159
Alright, I've just noticed it...

##lim_{a->b}\frac{tan\ a - tan\ b}{(1-\frac{a}{b})(1+tan\ a\ tan\ b)} = lim_{a->b}\frac{tan (a-b)}{(\frac{b-a}{b})} = -b##

Thanks for help!

Very well!
 

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