# Limits problem

## Homework Statement

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

## 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
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## Homework Statement

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

## 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##?

ah sorry, its x$\rightarrow∞$

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.

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

both tends to π/2