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TomLikesPhysics Group Title

lim_{x rightarrow infty} (-3x+sqrt{9x^2+4x-5}) The answer is apparently 2/3. But I can´t loose the squareroot term at any place so I always end up with infinity - infinity = 0. How do I do this limit right?

  • 2 years ago
  • 2 years ago

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  1. TomLikesPhysics Group Title
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    \[\lim_{x \rightarrow \infty} (-3x+\sqrt{9x^2+4x-5})\]

    • 2 years ago
  2. TomLikesPhysics Group Title
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    That is limit I am talking about.

    • 2 years ago
  3. shubhamsrg Group Title
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    rationalize it.. see if it it helps..which it should..

    • 2 years ago
  4. shubhamsrg Group Title
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    getting me ??

    • 2 years ago
  5. TomLikesPhysics Group Title
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    I guess... let me show your where I stuck right now.

    • 2 years ago
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  6. shubhamsrg Group Title
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    you're right till there.. now,, take x^2 common from the sqrt and in all,, x common from the denominator,, you see the solution now ?

    • 2 years ago
  7. TomLikesPhysics Group Title
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    I can not quite follow you here.

    • 2 years ago
  8. shubhamsrg Group Title
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    you have (4x)/(sqrt(9x^2 +4x -5) + 3x) = (4x)( x sqrt( 9 + 4/x - 5/x^2 ) + 3x following till here ?

    • 2 years ago
  9. TomLikesPhysics Group Title
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    yup

    • 2 years ago
  10. shubhamsrg Group Title
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    now,,x gets cancelled from numerator and denominator .. is much easier then right ?

    • 2 years ago
  11. TomLikesPhysics Group Title
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    Ah... now I understand. Thanks a lot shubhamsrg. I never thought of doing that one. :) thx

    • 2 years ago
  12. shubhamsrg Group Title
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    nevermind,,glad to help ! :)

    • 2 years ago
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