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November 2nd, 2009, 05:22 PM
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| |  Determine the limit and where possible compute.
hi, the problem i have is i'm having trouble with how to determine the limit using first principles, any help would be appreciated. the problem is..
lim (5x-2)^1/2 - 2(2^1/2)
x->2 (x^2)-(3x)+2
thanks for any help, i've never had much luck with limits |
November 2nd, 2009, 05:55 PM
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Quote:
Originally Posted by cpj  hi, the problem i have is i'm having trouble with how to determine the limit using first principles, any help would be appreciated. the problem is..
lim (5x-2)^1/2 - 2(2^1/2)
x->2 (x^2)-(3x)+2
thanks for any help, i've never had much luck with limits | Multiply numerator and denominator by the conjugate surd  , simplify the numerator, factorise the denominator, cancel the common factor and then take the limit. Please show your work if you need more help.
__________________ There are two things you should never try to prove: the impossible and the obvious. The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)
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November 3rd, 2009, 11:38 AM
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(5x-2)^1/2 - (8)^1/2
x^2 - 3x + 2
[(5x-2)^1/2 - (8)^1/2] * [(5x-2)^1/2 + (8)^1/2]
[(5x-2)^1/2 + (8)^1/2]*[(x^2)-3x+2]
(5x-2)-8
[(5x-2)^1/2 + (8)^1/2]*(x-1)(x-2)
5
-2(2^1/2)
this is my final limit, could you tell me if its correct please. i'm not sure.. |
November 3rd, 2009, 11:45 PM
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Quote:
Originally Posted by cpj (5x-2)^1/2 - (8)^1/2
x^2 - 3x + 2
[(5x-2)^1/2 - (8)^1/2] * [(5x-2)^1/2 + (8)^1/2]
[(5x-2)^1/2 + (8)^1/2]*[(x^2)-3x+2]
(5x-2)-8
[(5x-2)^1/2 + (8)^1/2]*(x-1)(x-2)
5
-2(2^1/2)
this is my final limit, could you tell me if its correct please. i'm not sure.. | I get  .
__________________ There are two things you should never try to prove: the impossible and the obvious. The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)
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