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    These are some practice questions I've attempted recently. They seem quite basic so I want to make sure I'm doing them right. There looks like there's a lot here but the questions are very short
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    (Original post by pineapplechemist)
    These are some practice questions I've attempted recently. They seem quite basic so I want to make sure I'm doing them right. There looks like there's a lot here but the questions are very short
    Just looked at the first picture.

    \epsilon can be any positive number. I chooes \epsilon=1 and your proof fails since it includes values of x greater than 1 in the |x-c| < delta bit.
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    (Original post by ghostwalker)
    Just looked at the first picture.

    \epsilon can be any positive number. I chooes \epsilon=1 and your proof fails since it includes values of x greater than 1 in the |x-c| < delta bit.
    Dow need to choose delta to equal 2^-100?
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    (Original post by pineapplechemist)
    Dow need to choose delta to equal 2^-100?
    You're thinking in the right direction. You can't let delta exceed, 2^-100.

    But what if I choose epsilon = 2^-200

    Edit: Minor correction.
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    As far as the other questions (warning, long list of niggles, but don't take it to heart - your answers are 90% of the way there in general).

    Firstly, I'll say that I think these "what is the largest value of delta ..." questions are a waste of time - miss the point IMHO, so in a way I don't really care what you do for them.

    That said, I'd say all of them should have at least the same amount of working given as you did for the one with x0=7, epsilon = 0.1.

    Also, use connectives. There should be a flow from one line to the next - it shouldn't look like you just threw a load of equations on the paper. Just putting "so" at the beginning of each line would help a lot:

    e.g. 7 < x^2 < 9,
    so \sqrt{7} &lt; x &lt; \sqrt{9} = 3, etc.

    When you have something like: \sqrt{99} &lt; x &lt; \sqrt{101}, you need to explain why you've chosen \delta = \sqrt{101} - 10 and not \delta = 10 - \sqrt{99}.

    There's a question where you say "x &lt; \sqrt{99}". Note that you ALSO need x &gt; -\sqrt{99}. It doesn't affect the answer here but you should show you haven't just forgotten this requirement.

    For the two "show f is everywhere cts" questions, you use a variable c without ever saying what it is. It would be better to start off with something like "Pick any c \in \mathbb{R}" and end with "So f is cts at c for any choice of c and so is cts everywhere".

    The line |x-c| &lt; \delta \implies |3x-3c| &lt; \epsilon / 3 is incorrect (delta is < epsilon /3 , but you've just multiplied by 3, so all you have is |3x-3c| < epsilon,

    META: I wish people would either use LaTeX or just plain text to post questions, rather than expecting people to look at attached photos, but if you must attach photos can you please try to get the camera pointing at some reasonable approximation to "square on" to the paper? And make sure the attachment is the right way up as well (I know the OP is not guilty of this, but it happens, a lot).
 
 
 
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