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

Answer:

Option c is answer

Step-by-step explanation:

A function is given as

$h(x) = \frac{2x^2-6x+1}{2+x-x^2}$

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

$h(x) = \frac{2-\frac{6}{x}+\frac{1}{x^2}  }{\frac{2}{x^2} +\frac{1}{x}-1 }$

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