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Math Help - limits question

  1. #1
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    limits question

    How can we know if the limits to these actually exist and if they do, what are they.

    1) lim (x---->0) {(sqrt(1+2x)) - (sqrt(1-3x))}/{x}

    2) lim (x---->1) {3(x^4) - 8(x^3) + 5}/{(x^3) - (x^2) -x -1}

    3) lim (x----->infinity) {(sqrt((x^2) +1) - (sqrt((x^2) -1)}
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  2. #2
    Senior Member BAdhi's Avatar
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    Can we see your attempt please? Because there is no use of just giving up the answers...
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  3. #3
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    1. Try rationalising the numerator.

    2. Divide numerator and denominator by the highest power of x.
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  4. #4
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    Quote Originally Posted by maximus101 View Post
    How can we know if the limits to these actually exist and if they do, what are they.

    1) lim (x---->0) {(sqrt(1+2x)) - (sqrt(1-3x))}/{x}
    Multiply both numerator and denominator by [tex]\sqrt{1+ 2x}+ \sqrt{1- 3x}

    2) lim (x---->1) {3(x^4) - 8(x^3) + 5}/{(x^3) - (x^2) -x -1}
    What is the value at x= 1?

    3) lim (x----->infinity) {(sqrt((x^2) +1) - (sqrt((x^2) -1)}
    multiply numerator and denominator by \sqrt{x^2+ 1}+ \sqrt{x^2- 1}

    These are essentiall "Pre-Calculus" problems. Strange that you would post them with Analysis problems.
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