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clara1223

  • one year ago

find the limit as x approaches 3 of (1)/(x-3)

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  1. clara1223
    • one year ago
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    \[\lim_{x \rightarrow 3}\frac{ 1 }{ x-3 }\]

  2. tkhunny
    • one year ago
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    What does the denominator do as x approaches 3?

  3. clara1223
    • one year ago
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    @tkhunny it becomes 0...?

  4. clara1223
    • one year ago
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    please help! i have this and one more limit problem and i'm done and ive been studying all day and im exhausted and I just don't understand these.

  5. jim_thompson5910
    • one year ago
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    I suggest looking at a table of values specifically x values close to x = 3 like x = 3.1, x = 3.01, x = 3.001 and x = 2.99, x = 2.999, x = 2.9999, etc

  6. jim_thompson5910
    • one year ago
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    |dw:1441074112182:dw|

  7. clara1223
    • one year ago
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    I already know that the limit doesnt exist I just need to know how to prove it

  8. jim_thompson5910
    • one year ago
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    |dw:1441074140948:dw|

  9. jim_thompson5910
    • one year ago
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    as x gets closer to 3 from the left side, the value of f(x) heads off to negative infinity so the left hand limit is equal to -infinity \[\Large \lim_{x \to 3^{-}}f(x) = -\infty\]

  10. jim_thompson5910
    • one year ago
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    as x gets closer to 3 from the right side, the value of f(x) heads off to positive infinity the right hand limit is equal to +infinity \[\Large \lim_{x \to 3^{+}}f(x) = +\infty\]

  11. jim_thompson5910
    • one year ago
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    LHL = left hand limit RHL = right hand limit since \[\Large LHL \ne RHL\] the limit at x = 3 itself does not exist the graph confirms this https://www.desmos.com/calculator/e09hafa0f1

  12. clara1223
    • one year ago
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    @jim_thompson5910 how would I prove this algebraically? is there a way to manipulate or sinplify 1/x-3?

  13. jim_thompson5910
    • one year ago
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    I don't know any way to prove it algebraically other than to use a table maybe

  14. clara1223
    • one year ago
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    @tkhunny do you know of any way to prove it algebraically?

  15. tkhunny
    • one year ago
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    x - 3 = 0 -- Solve.

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