Question

without graphing, how do you find the limits as the equation (2x^2 +3)/(5x^2 + 7) goes to positive and negative infinity without graphing? how do I support the claims

Answer 1

What is the degree of the numerator

Answer 2

\[2x ^{2}\]

Answer 3

two x squared

Answer 4

that's the leading term

Answer 5

the degree is the exponent

Answer 6

so the degree of the numerator is 2

Answer 7

the degree of the denominator is also 2

Answer 8

correct.

Answer 9

so because the two degrees are equal, you take the ratio of the leading terms

or the ratio of the leading coefficients

Answer 10

ok so that would be 2/5. so is that the horizontal asymptote?

Answer 11

yes

Answer 12

so this means that as x -->oo, then f(x) --> 2/5

Answer 13

similarly, as x -->-oo, f(x) --> 2/5

Answer 14

perfect thank you so much

Answer 15

np