√1+t-√1-t/t lim

Question

-----> 0
The answer is one and I am not getting it

I factored it like this √1+t-√1-t/t x √1+t-√1-t

Factoring it out further I got in the numerator
(1-t)(1+t) / t(√1+t+√1-t) how do you cancel further?

Answer 1

I am going to go out on a limb and guess that you meant:

lim ( √(1+t) - √(1-t) )/t , as t --->0

noting to factor here, you have to rationalize the numerator

= lim ( √(1+t) - √(1-t) )/t * (√(1+t) + √(1-t))/(√(1+t) + √(1-t))
= lim ( 1+t - (1 -t) )/(t(√(1+t) + √(1-t))
= lim 2t/(t(√(1+t) + √(1-t))
= lim 2/(√(1+t) + √(1-t)) as t ---> 0
= 2/(√1 + √1)
= 2/2
= 1

btw, did you clean up your previous post ?

Answer 2

yes i will now