Question

(a) Find horizontal and vertical asymptotes of f(x) = 2 + x 2 − 3x 6 x 6 − x 3

(b) Find lim x→−∞ −2x 5 − 3x 2 + x − 1 1 − x 3 − 3x 5

Answer 1

a)

we have

for horizontal asymptote,

here the highest order term in numerator is -3x⁶

and the highest order term in denominator is x⁶

so,

hence the horizontal asymptote is located at y = -3.

for vertical asymptote,

we must set denominator is equal to 0,

hence the vertical asymptote is located at x = 0

b)