# Limits problem

1. Jun 4, 2012

### pcm

1. The problem statement, all variables and given/known data
find:
lim x$\rightarrow0$ (x+2)tan-1(x+2)-xtan-1(x)

2. Relevant equations

3. The attempt at a solution
lim x$\rightarrow0$ (x+2)tan-1(x+2)-xtan-1(x)=
lim x$\rightarrow0$ [x(tan-1(x+2)-tan-1(x))+2tan-1(x+2)]
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jun 4, 2012

### LCKurtz

Your functions are all continuous. What happens if you plug in $x=0$?

3. Jun 4, 2012

### pcm

ah sorry, its x$\rightarrow∞$

4. Jun 4, 2012

### pcm

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. Jun 4, 2012

### Villyer

Focus on the tan-1(x) and tan-1(x+2). What are their limits as x goes to infinity?

6. Jun 4, 2012

### pcm

both tends to π/2