Quiz:Limit

ORIGINAL FULL PAGE: Limit
STUDY THE TOPIC AT MULTIPLE LEVELS:
ALSO CHECK OUT: Quiz (multiple choice questions to test your understanding) |Page with videos on the topic, both embedded and linked to

Definition for finite limit for finite function of one variable

Which of these is the correct interpretation of $\lim _{x\to c}f(x)=L$ in terms of the definition of limit?

	For every $\alpha >0$, there exists $\beta >0$ such that if $0<|x-c|<\alpha$, then $|f(x)-L|<\beta$.
	There exists $\alpha >0$ such that for every $\beta >0$, and $0<|x-c|<\alpha$, we have $|f(x)-L|<\beta$.
	For every $\alpha >0$, there exists $\beta >0$ such that if $0<|x-c|<\beta$, then $|f(x)-L|<\alpha$.
	There exists $\alpha > 0$ such that for every $\beta >0$ and $0<|x-c|<\beta$, we have $|f(x)-L|<\alpha$.
	None of the above