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

Question

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

eamier · Answer

yes.

anonymous · Answer

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

eamier · Answer

when 1/0 = infinity. you know this

eamier · Answer

by dividing each term by x^6 see what happen

eamier · Answer

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

anonymous · Answer

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?

eamier · Answer

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

anonymous · Answer

-ve? What does that mean?

eamier · Answer

sorry, its mean negative. it will be negative infinity

eamier · Answer

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eamier · Answer

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

anonymous · Answer

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

eamier · Answer

emm, dont know.

anonymous · Answer

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