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    If someone could show me how they solved the remaining two problems I'd be really grateful
    https://i.imgur.com/Rg4rj0o.jpg
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    (Original post by smelborp)
    If someone could show me how they solved the remaining two problems I'd be really grateful
    https://i.imgur.com/Rg4rj0o.jpg
    For the first, note that e.g.:

    |x+1| = \begin{cases} x+1 & x+1 \ge 0 \Rightarrow x \ge -1 \\ -(x+1) & x+1 < 0 \Rightarrow x < -1 \end{cases}

    and note also that, for this limit, you need only consider values of x close to -3. And similarly for x^2-4 of course.

    The same trick may also work for the other question, I haven't tried.

    [edit: you probably also want to compute the limit as \lim_{x \to 3+} and \lim_{x \to 3-} to check that they are the same]
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    (Original post by atsruser)
    For the first, note that e.g.:

    |x+1| = \begin{cases} x+1 & x+1 \ge 0 \Rightarrow x \ge -1 \\ -(x+1) & x+1 < 0 \Rightarrow x < -1 \end{cases}

    and note also that, for this limit, you need only consider values of x close to -3. And similarly for x^2-4 of course.

    The same trick may also work for the other question, I haven't tried.

    [edit: you probably also want to compute the limit as \lim_{x \to 3+} and \lim_{x \to 3-} to check that they are the same]
    The same trick applies for  \gamma (the second question) but you will need to apply another method as well as you obtain an indeterminate form.
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    (Original post by simon0)
    The same trick applies for  \gamma (the second question) but you will need to apply another method as well as you obtain an indeterminate form.
    These are all indeterminate forms.
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    (Original post by atsruser)
    These are all indeterminate forms.
    Sorry, I should have been mor eclear, I meant for the second question, after using your method and cancelling down, you still had a indeterminate form (unlike the first question which after canelling down).

    Sorry about that.
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    (Original post by simon0)
    Sorry, I should have been mor eclear, I meant for the second question, after using your method and cancelling down, you still had a indeterminate form (unlike the first question which after canelling down).

    Sorry about that.
    Oh I see. I haven't yet had a chance to try this question so I'll have a go tomorrow and see what happens.
 
 
 
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