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Mathematics 51 Online
OpenStudy (anonymous):

is this true? limit of x-->0+ of (x^2+x^3)/(x^3+x^6)=infinity

OpenStudy (eamier):

yes.

OpenStudy (anonymous):

are you sure? Why? Can you explain it to me? i am having a hard time understanding it.

OpenStudy (eamier):

when 1/0 = infinity. you know this

OpenStudy (eamier):

by dividing each term by x^6 see what happen

OpenStudy (eamier):

1/5<1/4<1/3<1/2....1/0.5...<1/0.05<...the value become larger when the denominator closer to 0.

OpenStudy (anonymous):

So if I understood correctly, this would be only for positive numbers right? For as \[\lim_{x \rightarrow 0} \] instead of \[\lim_{x \rightarrow 0+}\] it wouldn't be true?

OpenStudy (eamier):

if x approach 0 from the left, it will be -ve

OpenStudy (anonymous):

-ve? What does that mean?

OpenStudy (eamier):

sorry, its mean negative. it will be negative infinity

OpenStudy (eamier):

|dw:1343261801588:dw|

OpenStudy (eamier):

sorry my bad draw. the graph should look like that i think

OpenStudy (anonymous):

Does \[f(g(x))=-\infty \] if f(x)<0 and g(x) = infinity?

OpenStudy (eamier):

emm, dont know.

OpenStudy (anonymous):

ok thanks for you're help! I'll add you as a fan! lol I have no many calculus questions, I apologize.

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