Calculus 1?

Question

what is the limit of (sqrt 2-T) - (sqrt 2)/T as T~>0.
Please Explain and show steps if needed.

Answer 1

You need to multiply by the .... hm, I forgot the word. But basically, you change the sign in the middle.

You know you can't use direct substitution because if you plug in 0 for T, it will be undefined. So, you need to try something else.

(root(2 - T) - root2)/T * (root(2 - T) + root2)/(root(2 - T) + root2)

(2 - T - 2) / (T(root(2 - T) + root2)

-1/(root(2 - T) + root2)

Now, plug in 0 for T.

-1 / (2root2)

That's it.

Answer 2

You do this term by term
as T->0, term 1 approaches sqrt(2).
Since sqrt(2) is a constant, any constant/T as T->0 will "blow up"
Since the second term "blows up", the whole thing "blows up"

Answer 3

-infiniti as x->0+
+infiniti as x->0-