Evaluate the limit (3x+5)/(x^2+1), x->+infinity?

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limit (3x+5)/(x^2+1)    where x--> inf

Since the highest power is x^2, then we divide both functions by x^2

=> lim (3x+5)/lim(x^2+1) = lim x^2(3/x + 5/x^2) /limx^2(1+1/x^2)

==> lim (3/x + 5/x^2) / lim (1+1/x^2) = 0+0/1+0= 0

Then the limit when x--> inf is 0

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