Find the limit of arctan ( x/(x^2 -2x +1) ) as x approaches 1

Question

anonymous · Answer

Hint: $$\lim_{x \rightarrow \infty}\arctan(x)=\pi/2$$

anonymous · Answer

Is arctan (1/0) a defined value ?! Can we say that arctan(1/0)  =pi/2

anonymous · Answer

No, that's why we have to take the limit.

anonymous · Answer

@drawar I solved it using wolfram solver it gave me pi/2 the question is how ? Cuz if we substitute with one we will get arctan(1/0) is that some how =pi/2 ? http://m.wolframalpha.com/input/?i=lim+atan+%28%28x%29%2F%28x%5E2-2x%2B1%29%29+as+x-%3E1&x=0&y=0

hartnn · Answer

$\Large \lim \limits_{x \rightarrow 1}\arctan( ( x/(x^2 -2x +1) ))=\arctan(1/0) \=\Large \lim \limits_{x \rightarrow \infty}\arctan(x)=\pi/2$

anonymous · Answer

@hartnn so we switch it from x->1 to x->infinity cuz 1/0 is infinity ! Somehow  it makes sense , thank you smart friend !