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anonymous

  • 5 years ago

Show that the equation 2^x = 2 − x^2 has at least two real roots

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  1. anonymous
    • 5 years ago
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    Solve for 0, then factor.

  2. amistre64
    • 5 years ago
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    use the determinate..i think its called of the quad formula.... if its 0 only 1 root, if it (+) 2 roots, it its (-) imaginary roots

  3. anonymous
    • 5 years ago
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    but its 2^x an exponential fuction...so how to use quadratic here ?

  4. amistre64
    • 5 years ago
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    thought that was a typo lol

  5. myininaya
    • 5 years ago
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    its called the discriminant

  6. anonymous
    • 5 years ago
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    Same here.

  7. amistre64
    • 5 years ago
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    soooo close......

  8. myininaya
    • 5 years ago
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    b^2-4ac

  9. anonymous
    • 5 years ago
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    but how does discriminant help ?

  10. anonymous
    • 5 years ago
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    \[-x^2+2^x -2 = 0\]

  11. amistre64
    • 5 years ago
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    x^2 = -2^x +2 square root both sides?

  12. amistre64
    • 5 years ago
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    x = +-sqrt(-2^x +2)

  13. anonymous
    • 5 years ago
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    sry but i m still in a fix ....jeezzzzz

  14. amistre64
    • 5 years ago
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    that doesnt tell you the roots, but it might show that there are 2 of them :)

  15. anonymous
    • 5 years ago
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    ahh..got ya !!!

  16. anonymous
    • 5 years ago
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    hey but the roots can be complex by taking the roots???

  17. anonymous
    • 5 years ago
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    by taking the square root

  18. amistre64
    • 5 years ago
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    roots can be complex and most are... but the only one to concern yourself with are the "real" roots

  19. anonymous
    • 5 years ago
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    yes...when it was +- sqrt( 2- 2^x). that does not show that v r gonna get two real roots which is the question asking for?

  20. amistre64
    • 5 years ago
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    if you wanna limit your self to even values of x

  21. anonymous
    • 5 years ago
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    but there is no domain given in the question

  22. anonymous
    • 5 years ago
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    meanwhile i checked on wolfram alpha

  23. amistre64
    • 5 years ago
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    oh wait... is it (-2)^x or -(2^x)??

  24. anonymous
    • 5 years ago
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    they had a graph which cuts on two points

  25. anonymous
    • 5 years ago
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    the latter one

  26. amistre64
    • 5 years ago
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    maybe log rules would help

  27. anonymous
    • 5 years ago
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    would you know guys what is uniform continuity?

  28. amistre64
    • 5 years ago
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    log(2^x) = log(2-x^2) x log(2) = log(2-x^2) log(2) = log(2-x^2)^1/x 2 =xroot(2-x^2) ??

  29. amistre64
    • 5 years ago
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    uniform?... id have to look it up

  30. anonymous
    • 5 years ago
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    ok

  31. anonymous
    • 5 years ago
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    f(x) = sin x is continuous on R. Is it uniformly continuous on R?

  32. amistre64
    • 5 years ago
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    id vote yes, its periodic, repetitive, and constantly the "same"

  33. amistre64
    • 5 years ago
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    if "x" is a fraction that gets us back to integer exponents with the first question....

  34. anonymous
    • 5 years ago
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    http://www.wolframalpha.com/input/?i=2^x+%3D+2+%E2%88%92+x^2 check out that one for me plsssssss

  35. amistre64
    • 5 years ago
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    ..... yeah.....thats correct :)

  36. anonymous
    • 5 years ago
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    so u think graph would be enough?

  37. amistre64
    • 5 years ago
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    the graph itself is visual proof, the mathematical proof seems a but difficult to reach.

  38. anonymous
    • 5 years ago
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    yes...and the second question like you said or is there any better way?

  39. amistre64
    • 5 years ago
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    if you graph the sin function, it sounds as if it would fit a "uniform" continuity.

  40. anonymous
    • 5 years ago
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    yes...thank you.... can i ask you anything else or i m just pissing u off :(

  41. amistre64
    • 5 years ago
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    lol.... you can ask....i might not have an answer tho :)

  42. anonymous
    • 5 years ago
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    how to write pi as a symbol on computer?

  43. amistre64
    • 5 years ago
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    on any computer? or in here?

  44. anonymous
    • 5 years ago
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    any computer

  45. amistre64
    • 5 years ago
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    its the ascii code 227 i think, there should also be a character keyboard in your menu that will bring up a virtual keyboard to find it on

  46. anonymous
    • 5 years ago
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    yeah mayb in microsoft word ...they might have it ...thanx

  47. amistre64
    • 5 years ago
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    programs..accessories....system tools....character maap is where mine is

  48. anonymous
    • 5 years ago
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    hey let me check that one ...thanx

  49. amistre64
    • 5 years ago
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    П lol

  50. anonymous
    • 5 years ago
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    hey u got that...i might copy it n save it on word ...lol

  51. anonymous
    • 5 years ago
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    ППППППППППП hhahah

  52. amistre64
    • 5 years ago
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    Пп hehehe

  53. anonymous
    • 5 years ago
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    lim x->pi/3 ((3+2cosx)^1/2 - 2) / ln (1+sin3x) ??? whats ur views on that one?

  54. amistre64
    • 5 years ago
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    pi/3 = 60 degrees..... is [sqrt(3+2cos(x)) - 2] / ln(1+sin(3x)) right?

  55. anonymous
    • 5 years ago
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    exactly

  56. amistre64
    • 5 years ago
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    sqrt(3+2cos(60)) - 2 sqrt(3 + 2(1/2)) - 2 ------------------- = ----------------- ln(1+sin(180)) ln(1+0)

  57. anonymous
    • 5 years ago
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    but thats a limit question ...plugging in the values making it 0/0

  58. amistre64
    • 5 years ago
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    sqrt(4) - 2 0 --------- = --- ln(1) 0 I see the dellima

  59. amistre64
    • 5 years ago
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    the derivative of each would be....

  60. amistre64
    • 5 years ago
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    Dx(ln(x)) = 1/x Dx(ln(1+sin(3x))) = 3cos(3x)/1+sin(3x) the reciprocal of that is what youll need

  61. amistre64
    • 5 years ago
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    Dx(sqrt(3+2cos(x))-2) = -sin(x)/sqrt(3+2cos(x))

  62. amistre64
    • 5 years ago
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    -sin(x) (1+sin(3x)) ---------------------- sqrt(3+2cos(x)) (3cos(3x)

  63. anonymous
    • 5 years ago
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    yes i was also somewhere there

  64. amistre64
    • 5 years ago
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    -sqrt(3) sqrt(3) --------- = -------- is what I get 2(3)(-1)(2) 12

  65. anonymous
    • 5 years ago
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    i have got 1/4sqrt3

  66. amistre64
    • 5 years ago
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    same thing, rationalize your denominator

  67. amistre64
    • 5 years ago
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    sqrt(3)/4(3)

  68. anonymous
    • 5 years ago
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    got ya !!! u must b a teacher for sure ... aren't u ?

  69. amistre64
    • 5 years ago
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    lol ..... nope, just an unemployed carpenter

  70. anonymous
    • 5 years ago
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    wtf??? impossible ...to me u r a GREAT TEACHER !!!! and more of a great human being

  71. amistre64
    • 5 years ago
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    thanx :)

  72. anonymous
    • 5 years ago
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    u have been so helpful...these questions were all for my next week homwork assignment...now i m so relaxed...thanx bro....really appreciate ur help

  73. anonymous
    • 5 years ago
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    Refer to the attachment.

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