Evaluate the limit of the function y if x goes to infinite? y=(3x^2-4x+1)/(-8x^2+5)

Since the values of x approach infinite, we'll calculate
the limit by factorizing both, numerator and denominator, by x^2, to create strings
whose limits is zero:

lim (3x^2-4x+1)/(-8x^2+5) = lim
x^2(3-5/x+1/x^2)/x^2(-8+5/x^2)

We'll reduce both, numerator
and denominator, by x^2:

lim
(3-5/x+1/x^2)/(-8+5/x^2)

We'll replace x by
infinite:

lim (3-5/x+1/x^2)/(-8+5/x^2) = [lim3-lim (5/x)+
lim(1/x^2)]/[lim(-8) + lim(5/x^2)] = (3 - 5/infinite + 1/infinite)/(-8 +
5/infinite)

lim (3x^2-4x+1)/(-8x^2+5) =
(3-0+0)/(-8+0)

lim (3x^2-4x+1)/(-8x^2+5) =
-3/8

We notice that the limit is the ratio of leding
coefficients of numerator and
denominator.

The requested limit of the
function is: lim (3x^2-4x+1)/(-8x^2+5) = -3/8.