Question

Find the limit if it exist

Answer 1

\[\lim_{x \rightarrow \infty} \frac{ (3x+1)^2 (4x-5)^2 }{ x^2(x^2-4x+3)(2x+1)^2 }\]

Answer 2

The degree of the numerator is 4
The degree of the denominator 6
So what do you think the limit is?

Answer 3

A polynomial near infinity behaves like the term of highest degree.
The numerator behaves like \( a x^4\)
The numerator behaves like \( b x^6\)
So the ration behaves like \[
\frac {a x^4}{b x^6}=\frac {a }{b x^2}
\]
where a and b are non zero constants.
What is the limit when x approaches infinity?

Answer 4

ration =ratio ( misprint)

Answer 5

What is the
\[
\lim_{n\to \infty} \frac {a} { b \, x^2}

\]?

Answer 6

The limit is obviously zero.