Struggling with Calculus Problems: Where to Find Help?

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1. http://s24.postimg.org/jdd9l8ayd/q8q_a.jpg
2. http://s24.postimg.org/z04iyloqd/q1q_a.jpg
3. http://s24.postimg.org/oeknmliet/q2q.jpg
4. http://s24.postimg.org/puw64qlbp/q6q.jpg




Questions are in the links above.



I completed 4 out of the 8 problems. I just don't know how to do these (As in I know what I'm doing is wrong).
 
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What don't you understand about problem 1? Establish continuity between the two parts by selecting k Hint: The value of f(3) must be the same when approaching x = 3 from the right and the left.

2. A plot is required.

3. After making the plot for 2, evaluate the limits.

4. Evaluate the limit.

IMO, these are very simple problems.
 
4 would be 0 correct?
 
Jonny B said:
1. http://s24.postimg.org/jdd9l8ayd/q8q_a.jpg
attachment.php?attachmentid=57601&stc=1&d=1365370992.jpg


2. http://s24.postimg.org/z04iyloqd/q1q_a.jpg

3. http://s24.postimg.org/oeknmliet/q2q.jpg

4. http://s24.postimg.org/puw64qlbp/q6q.jpg

attachment.php?attachmentid=57604&stc=1&d=1365371157.jpg


Questions are in the links above.

I completed 4 out of the 8 problems. I just don't know how to do these (As in I know what I'm doing is wrong).
Hello Jonny B. Welcome to PF !

According to the rules of this Forum, you need to show what you've tried before we can help you.

Also, you should include no more than two problems per thread.

The answer to #4 is zero.Added in Edit:
I do notice now that #2, and #3 are closely related.
 

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#2:
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#3.
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Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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