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

Answer:

Option b is right.

Step-by-step explanation:

A function is given as

$g(x) = \frac{x^2}{x^2-2x-1}$

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

$g(x) =\frac{\frac{1}{x^2} }{1-\frac{2}{x} -\frac{1}{x^2} }$

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