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anonymous

  • one year ago

I need help finding this limit.

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  1. anonymous
    • one year ago
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    \[\lim_{x \rightarrow 0} \left( x+Deltax^2-2(x+Deltax)+1-(x^2+2x+1)/Deltax \right)\]

  2. anonymous
    • one year ago
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    this? \[\lim_{x \rightarrow 0} \left( \frac{(x+\Delta x)^2-2(x+\Delta x)+1-(x^2+2x+1)}{\Delta x} \right)\]

  3. anonymous
    • one year ago
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    Yes, sorry for not inputting it correctly.

  4. thomas5267
    • one year ago
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    \(\Delta\) can be inputed by typing \Delta

  5. anonymous
    • one year ago
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    Thank you!

  6. thomas5267
    • one year ago
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    Put a space after the command so the software can recognize it.

  7. anonymous
    • one year ago
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    np. and is \(x\) or \(\Delta x\) approaching 0?

  8. anonymous
    • one year ago
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    just x is approaching 0, not \Delta

  9. thomas5267
    • one year ago
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    \frac{a}{b} \[ \frac{a}{b} \] \lim_{x \to 0} \left( \frac{x+\Delta x^2-2(x+\Delta x)+1-(x^2+2x+1)}{\Delta x} \right) \[ \lim_{x \to 0} \left( \frac{x+\Delta x^2-2(x+\Delta x)+1-(x^2+2x+1)}{\Delta x} \right) \]

  10. thomas5267
    • one year ago
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    Does the limit has anything to do with derivatives? This is the definition of the derivative except the definition of the derivative has \(\Delta x\to 0\) not \(x\to 0\).

  11. anonymous
    • one year ago
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    It looked like the definition of the derivative, but it would have to be \(\Delta x\) approaching 0

  12. anonymous
    • one year ago
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    Oh, I'm sorry, it is \[\Delta x\]

  13. anonymous
    • one year ago
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    ok, so you should start by multiplying everything out in the numerator. Using foil and distribution.

  14. anonymous
    • one year ago
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    Okay, I'll start out by doing that and but what am I going to do about \[\Delta x\]

  15. anonymous
    • one year ago
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    Treat it as just another variable. For example that middle term would be \[-2(x +\Delta x)= -2x-2\Delta x\]

  16. anonymous
    • one year ago
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    Oh okay, so we wouldn't be doing final minus initial. That's what I was confused about. Thank you so much!

  17. anonymous
    • one year ago
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    you're welcome. keep it as \(\Delta x\) because once you're done simplifying the numerator, the denominator will cancle out

  18. anonymous
    • one year ago
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    Do you know how to find limits by looking at a graph and discussing the continuity of the function? I'm lost on a (1-6) on this page in my textbook.

  19. anonymous
    • one year ago
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    Do you know how to find limits by looking at a graph and discussing the continuity of the function? I'm lost on a (1-6) on this page in my textbook.

  20. anonymous
    • one year ago
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    Do you know how to find limits by looking at a graph and discussing the continuity of the function? I'm lost on a (1-6) on this page in my textbook.

  21. anonymous
    • one year ago
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    can you post the picture?

  22. anonymous
    • one year ago
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    yes, one moment, my school's internet is very slow.

  23. anonymous
    • one year ago
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    I'm sorry for some reason, it just won't send, but I have to go to class. I'll ask my instructor and see if he can clarify. Thank you so much for all your help, it really means a lot to me!

  24. anonymous
    • one year ago
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    you're welcome

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