Question

EVALUATE ALGEBRAICALLY LIM 3X^2 +2X -2/ 2X^2 - 1 AS X GOES TO INFINITY

Answer 1

try this again....

Use the largest exponent value of "x" from the denominator to divide everything you have. In your case, it is (x^2)

top: 3x^2/x^2 +2x/x^2 -2/x^2
becomes: 3 +2/x -2/x^2 --toss away anything with an x in the denominator because it goes to 0 as x goes to infinity.

top = 3

bottom: 2x^2/x^2 -1/x^2
becomes: 2 -1/x^2 -- toss out anything with an x in the denominator because it will go to 0 as x goes to infinity.

bottom = 2

so the limit is (3/2) as x --> infinity

Answer 2

Rules that you discover are:

If the highest exponent of "x" is in the bottom; the limit =0

example: 2x/3x^2 has a limit of 0

If the highest exponent is the same from top to bottom; the limit is the value of the leading cooeficients.

Example: 5x^3/3x^3 limit is 5/3

If highest exponent is on top; then you have an "oblique" asymptote (kind of a limit but not).

example: 6x^2/2x = 6x as an asymptote. the ends of the graph will approach a line of (y=6x)

Answer 3

THANK YOU U MAKE IT VERY CLEAR TO ME