Limit question, why can't Mathway answer it?

Why can't mathway answer this???

Limit (sqrt(0.25x^2+1)-1)/(0.5x)

x → inf

1 Answer

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  • kb
    Lv 7
    8 years ago
    Favorite Answer

    lim(x→∞) [√(0.25x^2 + 1) - 1]/(0.5x)

    = lim(x→∞) [√(0.25x^2 + 1) - 1] * [(√(0.25x^2 + 1) + 1] / {0.5x [(√(0.25x^2 + 1) + 1]} via conjugates

    = lim(x→∞) [(0.25x^2 + 1) - 1] / {0.5x [(√(0.25x^2 + 1) + 1]}

    = lim(x→∞) 0.5x / [(√(0.25x^2 + 1) + 1].

    Now, divide each term by x = √x^2:

    lim(x→∞) 0.5 / [(√(0.25 + 1/x^2) + 1/x]

    = 0.5 / [(√(0.25 + 0) + 0]

    = 1.

    I hope this helps!

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