Thread: Limits!!!

First post!!! I have two questions guys (and girls)

Seeing as how these questions are so hard to write down in posts I have uploaded an image of them.

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1) Let the function f(x) be defined by

f(x) = 1/6((sqrt(x) -1)/(sqrt(x^2-1))) + (sqrt(7x)+sqrt(7))/(3(sqrt(x+3))) + x/6(sqrt((x-1)/(x^2-1)))

It can be shown that
f(1.1) approximately equals 1.05891
f(1.01) approximately equals 1.00982
f(1.001) approximately equals 1.00205

Find the exact value of f(x) as x approaches 1 from the right(1+) (so lim x->1+ f(x)
The + is part of the 1,meaning as x approaches 1 from the right)

My answer for this is (2sqrt(7)+sqrt(1/2))/6. Is this right? If not what is the right anwer and how to do it?

2) Use the squeeze theorem to prove that the limit of

x(sin^2(1/x)) = 0

as x approaches 0

Can somebody show me how to do this? I really need help on this one!!!

Thanks in advance

1) I think your answer is correct.

2) Since , you then have
Apply Squeeze Theorem from here.

Roy