## needhelp07 Group Title evaluate the limits one year ago one year ago

1. needhelp07 Group Title

$\lim_{x \rightarrow \infty}(\frac{ x ^{3}-1 }{ x ^{4}+1 })$

2. shining Group Title

easily consider the highest rate of varaiabe seperately in nominator and denominator lim x^3/x^4 = 0

3. needhelp07 Group Title

how did u do that??

4. shining Group Title

i said you should just put the highest power of varaiable instead of up and down (because the limit approaches infinity) so$\lim \frac{ x^{3} }{ x^{4}? }$=0 because x^4 > x^3

5. needhelp07 Group Title

what happens to -1 and +1 ?? is it cancelled out?? sorry if i have many questions

6. shining Group Title

you shoul eliminate them because in the limits of fraction like this type constants have no touchable influence

7. needhelp07 Group Title

ahh ok

8. Shanks Group Title

you can understand this by taking x^2 and x^4 common as follows: => $\lim_{x \rightarrow \infty} \left( \frac{ x^{2} ( 1- \frac{ 1 }{x^{2}}) }{ x^{4} ( 1+ \frac{ 1 }{x^{4}}) } \right)$ Further strike out and reduce it to $\lim_{x \rightarrow \infty} \left( \frac{( 1- \frac{ 1 }{x^{2}}) }{ x^{2} ( 1+ \frac{ 1 }{x^{4}}) } \right)$ Obviously 1/x^2 and 1/x^4 when x-> infinity will be = 0 So inside bracket fraction becomes 1/1. and 1/x^2 = 0 when x-> infinity Thereby, given lim = 0