Question

Use the limit theorem and the properties of limits to find the horizontal asymptotes of the graph of the function h(x) = 2x2-6x+1/2+x-x2

Answer 1

Option c is answer

Explanation:

A function is given as

`h(x) = (2x^2-6x+1)/(2+x-x^2)`

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 2 and -1 respectively

Asymtote would be y =2/-1 = -2

Alternate method:

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

`h(x) = (2-(6)/(x)+(1)/(x^2)  )/((2)/(x^2) +(1)/(x)-1 )`

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 2/-1 =-2

Hence horizontal asymptote is y =-2