Finding Limit of x as it Approaches 0

[pcm]

Homework Statement

find:
lim x$\rightarrow0$ (x+2)tan^-1(x+2)-xtan^-1(x)

Homework Equations

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)]

 

[LCKurtz]

Homework Statement

find:
lim x$\rightarrow0$ (x+2)tan^-1(x+2)-xtan^-1(x)

Homework Equations

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)]

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

 

[pcm]

ah sorry, its x$\rightarrow∞$

 

[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.

 

[Villyer]

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

 

[pcm]

both tends to π/2