I need help solving what I think is a pretty simple limits questions, but I just can't see where to start.
I need to find:
the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)
and the lim as x goes to zero of the same function
Please help!
I need help solving what I think is a pretty simple limits questions, but I just can't see where to start.
I need to find:
the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)
and the lim as x goes to zero of the same function
Please help!
When taking the limit of a rational expression, if x approaches +/- infinity, you can disregard all but the coefficients of the highest powers.
Therefore you have,
$\displaystyle \lim_{x\to\infty}\frac{3x^{2}}{4x^{2}}$
Now, you can see what it is?.
As x approaches 0, look close, can you see it?.
Divide the numerator and denominator by $\displaystyle x^2$Originally Posted by afn2
$\displaystyle \lim_{x\to\infty}\frac{3+\frac{2}{x}+\frac{2}{x^2} }{4+\frac{2}{x}+\frac{7}{x^2}}$
The numerator is,
$\displaystyle \lim_{x\to\infty} 3+\frac{2}{x}+\frac{2}{x^2}=3$
The denominaot is,
$\displaystyle \lim_{x\to\infty}4+\frac{2}{x}+\frac{7}{x^2}=4$
Since both limits exists thus the value of the limit is 3/4
The limit as x goes to 0 should be simple. Both the numerator and denominator are continous functions on all real numbers (ie. the domain in both cases is all real numbers) and the denominator is not 0 for x = 0, so effectively all you need to do is substitute 0 for x in the expression.Originally Posted by afn2
-Dan