Limits problem

  • Thread starter pcm
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  • #1
pcm
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Homework Statement


find:
lim x[itex]\rightarrow0[/itex] (x+2)tan-1(x+2)-xtan-1(x)


Homework Equations





The Attempt at a Solution


lim x[itex]\rightarrow0[/itex] (x+2)tan-1(x+2)-xtan-1(x)=
lim x[itex]\rightarrow0[/itex] [x(tan-1(x+2)-tan-1(x))+2tan-1(x+2)]

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
LCKurtz
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Homework Statement


find:
lim x[itex]\rightarrow0[/itex] (x+2)tan-1(x+2)-xtan-1(x)


Homework Equations





The Attempt at a Solution


lim x[itex]\rightarrow0[/itex] (x+2)tan-1(x+2)-xtan-1(x)=
lim x[itex]\rightarrow0[/itex] [x(tan-1(x+2)-tan-1(x))+2tan-1(x+2)]

Your functions are all continuous. What happens if you plug in ##x=0##?
 
  • #3
pcm
76
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ah sorry, its x[itex]\rightarrow∞[/itex]
 
  • #4
pcm
76
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x(tan-1(x+2)-tan-1(x))
this part can be evaluated using l hopital(?),but it requires multiple use of rule.
i am expecting kind of trigonometric solution.
 
  • #5
294
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Focus on the tan-1(x) and tan-1(x+2). What are their limits as x goes to infinity?
 
  • #6
pcm
76
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both tends to π/2
 

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