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Math Help - couple calc questions need work! cant get correct answer help please!

  1. #1
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    couple calc questions need work! cant get correct answer help please!

    limit x-> -1 of cubed rt (3x-5/25x-2)
    not sure how to go about this at all


    i think the answer is 2/3 but i cant work it up




    lim x->0 √(3x+2) - √2
    x




    r(x)= |3x| A) lim x->0 of r(x) question 2 B) r(0)
    x
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  2. #2
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    Re: couple calc questions need work! cant get correct answer help please!

    these werent formatted right. the middle one the x is underneath the top term as well as for the absolute (|3x|)/x

    also, i tried to multiply the middle one by its conjugate √(3x+2) - √2

    i wind up getting (3x)/(x (√(3x+2) - √2) ) i think thats the right track but im not sure
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  3. #3
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    Re: couple calc questions need work! cant get correct answer help please!

    The first one you can just plug in -1 for x:

    \lim_{x \rightarrow -1} \sqrt[3]{ \frac{3x-5}{25x-2}}=\sqrt[3]{ \frac{3(-1)-5}{25(-1)-2}}


    The second one you were almost there:

    \lim_{x \rightarrow 0} \frac {\sqrt{3x+2} - \sqrt{2}}{x}=\lim_{x \rightarrow 0} \frac {(\sqrt{3x+2} - \sqrt{2})(\sqrt{3x+2} + \sqrt{2})}{x(\sqrt{3x+2} + \sqrt{2})}=\lim_{x \rightarrow 0} \frac{3x}{x(\sqrt{3x+2} + \sqrt{2})}

    So....... can it be simplified any further?


    For the third one, you look at the limit as x approaches 0 from the right and from the left. If they're the same, that's the limit, and if they're different, the limit doesn't exist. So what is |3x| in terms of x when x<0 and what is it when x>0? Remember x is negative in the x<0 case.

    \lim_{x \rightarrow 0}\frac{|3x|}{x}

    Of course r(0) is undefined.

    - Hollywood
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