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On this problem, I'm not sure what Big O definition they are referring. How would the big o definition help show this?

Use the definition of $O$ to show that if $y = y_h + O(h^p)$, then $hy = hy_h + O(h^{p+1})$.

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The first statement is saying, taking big O as $x$ approaches some $a$ for some $M>0$ $$ |y-y_h|0$.

Now what happens if you multiply the LHS by $\frac{|h|}{|h|}=1$?

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    I'm quite lost in this topic..I don't understand any of what you just wrote and can't really answer the question :( – 2017-01-21
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    @john I didn't write much more than the definition of what it means to be big o of something so maybe start with that – 2017-01-21