Question

Use the limit theorem and the properties of limits to find the horizontal asymptotes of the graph of the function g(x) = x2/x2-2x-1

Answer 1

Option b is right.

Explanation:

A function is given as

`g(x) = (x^2)/(x^2-2x-1)`

Limit is to be found out for x tends to infinity.

We find that numerator and denominator has the same degree.

HEnce a horizontal asymptote exists

COefficients of leading terms are 1 and 1 respectively

Asymtote would be y =1/11 = 1

Alternate method:

When x tends to infinity, 1/x tends to 0

`g(x) =((1)/(x^2) )/(1-(2)/(x) -(1)/(x^2) )`

by dividing both numerator and denominator by square of x.

Now take limit as 1/x tends to 0

we get

limit is y tends to 1/1 =1

Hence horizontal asymptote is y =1