QUESTIONS - FUNCTIONS

QUESTIONS - ANSWERS - FUNCTIONS
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Determine the horizontal asymptote of the following rational function? f(x) = 4x / (x2 – 3)
HORIZONTAL ASYMPTOTE IS OBTAINED BY FINDING LIMIT OF Y AS X TENDS TO INFINITY.
HERE WE HAVE LIMIT AS ZERO SINCE
4X/(X^2-3) = 4/[X-(3/X)]...WHICH TENDS TO ZERO AS X TENDS TO INFINITY.
HENCE Y=0 THAT IS THE X AXIS IS A HORIZONTAL ASYMPTOTE.

what kind of asymptote occurs for the following rational function? f(x) = (10x³ + x²) / [ 4(x² - 1) ]

1.VERTICAL ASYMPTOTES:

Y TENDS TO INFINITY AS X TENDS TO + OR -1 .
HENCE
X=1 AND X=-1 ARE THE 2 VERTICAL ASYMPTOTES.

2.HORIZONTAL ASYMPTOTE:

AS X TENDS TO INFINITY Y TENDS TO INFINITY.HENCE THERE IS NO H.A.

3.INCLINED ASYMPTOTE:-
A.RIGHT LINE
Y/X = (10X^3+X^2)/(4X^3-X)=[10+(1/X)]/[4-(1/X^2)] TENDS TO 10/4 = 2.5 = K SAY
AS X TENDS TO +INFINITY.
Y-KX = [(10X^2+X)/(4X^2-1)]-2.5X = [10X^2+X-2.5X(4X^2-1)]/[4X^2-1]
=(3.5X)/(4X^2-1)...TENDS TO ZERO = L SAY.. AS X TEND TO +INFINITY.
HENCE THERE IS AN INCLINED ASYMPTOTE GIVEN BY
Y=KX+L=2.5X+0=2.5X
B.LEFT LINE.
WE FIND SAME LIMITS AS ABOVE FOR X TENDING TO -INFINITY.HENCE THERE
IS NO LEFT INCLINED ASYMPTOTE.