Question

I need help with this:
lim(x^2+x+1)/(2x^2-3), x->infinity

Answer 1

lim(x^2+x+1)/(2x^2-3),x\[\rightarrow \infty \]
divide the numerator & denominator by x^2
\[\lim_{x \rightarrow \infty} \frac{ \frac{ x ^{2+x+1} }{x ^{2} }}{ \frac{ 2x ^{2}-3 }{x ^{2}} } = \]\[\lim_{x \rightarrow \infty} \frac{ 1+x/x ^{2}+\frac{ 1 }{ x ^{2} } }{ 2-\frac{ 3 }{x ^{2} } } \]\[\lim_{x \rightarrow \infty} \frac{ 1+\frac{ 1 }{ x }+\frac{ 1 }{ x ^{2} } }{ 2-\frac{ 3 }{ x ^{2} } }\]
\[\lim_{x \rightarrow \infty} \frac{ 1 }{ x}\rightarrow 0\]\[\lim_{x \rightarrow \infty} \frac{ 1 }{ x ^{2} } \rightarrow 0\]
=\[\frac{ 1+0+0 }{ 2-0}=\frac{ 1 }{ 2 }\]

Answer 2

thank you. Greate help.