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Faz
Lv 7
Faz asked in Science & MathematicsMathematics · 1 decade ago

Find the Limit question?

I came across this question. Evaluate the limit:

lim x-->∞ (8x -√(64x²+6x))

I understand that you would multiply by the conjugate to obtain:

= lim x-->∞ -6x / (8x + √(64x²+6x))

How do you proceed from here with the denominator - how do you factor the x out?

Update:

All I could get with the denominator was

8x + √2 √(x(3+32x))

Update 2:

Nice one guys, thanks.

3 Answers

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  • ted s
    Lv 7
    1 decade ago
    Favorite Answer

    Note: √ ( 64 x² + 6x ) = √ ( [x²][64 + 6 / x] ) = | x | √(64 + 6 / x) and since x ---> ∞ ., | x | = x

  • Avinash
    Lv 7
    1 decade ago

    = lim x-->∞ -6x / (8x + √(64x²+6x))

    Divide the numerator and the denominator by x:

    = lim x-->∞ -6 / (8 + √(64+6/x))

    = -6/(8 + √64+0)) (because lim x--> ∞ (1/x) = 0)

    = -6/(8 + 8)

    = -6/16

    = -3/8

    Ans: -3/8

    __________________.

  • Anonymous
    1 decade ago

    I look at this...and still cannot believe i got a 5 on the calc ap haha

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