Find the horizontal asymptote of the graph
2 answers:
Answer:
Step-by-step explanation:
We are given that a fundtion
We have to find the horizontal asymptote of the given function
We know that when degree of numerator and degree of denominator are equal then to get horizontal asymptote we divide the coefficient of heighest power of x in numerator by the coefficient of heighest power of x in denominator .
There are degree of both numerator and denominator are same .
Therefore, horizontal asymptote=
Horizontal asymptote=
Hence, the horizontal asymptote of given graph =
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Prove:
Using mathemetical induction:
P(n) =
for n=1
P(n) = = 6
It is divisible by 2 and 3
Now, for n=k,
P(k) =
Assuming P(k) is divisible by 2 and 3:
Now, for n=k+1:
P(k+1) =
P(k+1) =
P(k+1) =
Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also
divisible by 2 and 3.
Hence, by mathematical induction, P(n) = is divisible by 2 and 3 for all positive integer n.