Evaluate the limit of function (7x^2+5x)/(8x^3+6x), x-->infinity.

To evaluate the limit of the rational function, when x tends to +inf.,we'll factorize both, numerator and denominator, by the highest power of x, which in this case is x^3.

We'll have:

lim (7x^2+5x)/(8x^3+6x) = lim (7x^2+5x)/lim (8x^3+6x)

lim (7x^2+5x)/lim (8x^3+6x)  = lim x^3*(7/x + 5/x^2)/lim x^3*(8 + 6/x^2)

After reducing similar terms, we'll get:

lim (7/x + 5/x^2)/lim (8 + 6/x^2)= (0+0)/(8+0)= 0/8= 0.