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I'm doing some practice problems and I am stuck on the following limits.

**1) Limit as x approaches infinity of (sin^2(x))/x^2**

Now for this one I thought that the answer would just be 1 seeing as the limit of sinx/x is 1, however the answer is apparently 0 and I can't see the reasoning for this.

**2) Limit as x approaches 0 of (cosx-1)/xsinx**

Now for this one I first tried getting an the identity for sin^2x out of it by squaring it but that didn't work. Then I just tried breaking it up, but I just keep ending up getting 0 but apparently the answer is 1/2.

**3) Limit as x approaches pi/3 of (cosx-1/2)/(x-pi/3)**

Again I am totally lost. I keep wanting to try and get an identity out of it but I just cant get anything useful.

**4) Now this question I know should be easy. I am just having trouble understanding where to start. If F(x) = the integral of f(t)dt (the values on the integral are b=x and a=1) and f(t)= integral (squareroot(1+u^2))/u *du . Find F''(3).**

Apparently the answer to this is (2squareroot82)/3

If this isn't clear I can always draw it out and post it, I'm sure that what I tryed to type isn't overly clear.

Sorry about these questions guys, I know I haven't exactly shown a lot of work, but these are the ones that I have no idea of how to do, I've been attempting them for 2 days now and just can't seem to get anywhere