If f:R/{1,-1} -> R, f(x) = arctg[1/(x^2 - 1) calculate lim f(x) = ? when x->1 , x>1.
3 Answers
hala718 | High School Teacher | (Level 1) Educator Emeritus
lim f(X) = lim arctg (1/(1-x^2) when x-->1
Substitute with x=1
lim f(x) = arctg lim (1/0)
But we know that arctg = arcsin/arccos
==> arctg (1/0) = arc(sin(pi/2)/cos(pi/2)
= arctg(pi/2)
= pi/2
neela | High School Teacher | (Level 3) Valedictorian
To find the lt arc(1/x^2-1) as x--> 1+
Solution:
We know that lt tan (x)-) asx-->(pi/2- ) is infinity. Therefore,
{Lt arc tan 1/(x^2-1) as x--> 1 } = lt arc tan ((pi/2)-) = pi/2.
giorgiana1976 | College Teacher | (Level 3) Valedictorian
lim arctg [1/(x^2 - 1)] = arctg lim [1/(x^2 - 1)] =
x -> 1 x -> 1
x > 1 x > 1
lim f(x) = arctg 1/(1-1) = arctg(1/+0) = arctg (inf) = pi/2