lim

Question

t--->0
square rooted (1+t) - square rooted (1-t)/t

this is what i have so far is the conjugates of the square root of 1+t and 1-t

which would be square root of 1+t + square root of 1-t/t(square rooted (1+t)(1-t)

the numerator is not canceling out.......

Answer 1

do you mean

(√(1+t)-√(1-t))/t ?

That is indeed 0/0

"rationalizing" the numerator, we have

(√(1+t)-√(1-t))(√(1+t)+√(1-t))
--------------------------------
t (√(1+t)+√(1-t))

(1+t)-(1-t)
----------------
t (√(1+t)+√(1-t))

--> 2/(1*(√2+0)) = 2/√2 = √2