Is Finding a Common Denominator Necessary for Evaluating This Limit?

[Lizwi]

How do I evaluate this limit I have no Idea, I'm sorry for not showing my work please!

lim_{x\rightarrow0} \frac{1}{sin²x} +\frac{1}{x²}

 

[algebrat]

Doesn't it go to infinity?

 

[Infinitum]

What happens when you have...

lim_{x\to 0^+} \frac {1}{x}

That is a basic limit, answering that should lead you to what you want.

 

[Bohrok]

When using itex, you wouldn't use the other tags that the board uses such as for superscripts; you would use ^ to make exponents.

Could you have meant this limit with subtraction instead?
\lim_{x\to 0}\frac{1}{\sin^2x} - \frac{1}{x^2}

 

[DonAntonio]

How do I evaluate this limit I have no Idea, I'm sorry for not showing my work please!

\lim_{x\to 0}\left(\frac{1}{sin^2x}+\frac{1}{x^2}\right)

I already edited your post above. Now read the other posts.

DonAntonio

 

[ME_student]

I have not taken calc yet, but would he need to find a common denominator?

 

[DonAntonio]

I have not taken calc yet, but would he need to find a common denominator?

Kudos for the courage to post without having yet studied calculus..:) In this case it isn't needed to find

common denominator as: (1) both parts of the expression are positive, (2) it's a sum and (3) both tend to \infty as x\to 0

DonAntonio