Recall that a slant (oblique) asymptote occurs when the degree of the poly- nomial in the numerator is one higher than that of the polynomial in the de- nominator. For example, y = (x^3 + x + 1) / (x^2 - 1) = x - (2x - 1) / (x^2 - 1) has a slant asymptote y = x. Find the slant asymptote of the following function: y = (x^3 + 3x^2 + 2x + 1) / (x^2 + 1)
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The given function is: $$ f(x) = \frac{3x^2 + 2x + 1}{x} $$ The degree of the polynomial in the numerator is 2 (since the highest power of x is $x^2$), and the degree of the polynomial in the denominator is 1 (since the highest power of x is $x$). Since the Show more…
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