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For f(x)=(3x^2-5x+2)/(2x^2-6) complete the statements.

f(x)->_________ as x->-infinity
f(x)->_________ as x->infinity

In the blanks, I say for the first one infinity then -infinity for the second one.

  • Calculus -

    use an intuitive approach.
    as x becomes "very large" your numerator is dominated by the 3x^2 term and your denominator is dominated by the 2x^2 term, the other terms become less and less significant as x gets bigger

    so your function approaches f(x) = 3x^2/2x^2 = 3/2

    so the limit is 3/2

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