anonymous one year ago Find the indicated limit, if it exists. @phi @solomonzelman @jdoe0001 @paki @aaronq @zepdrix @e.mccormick @thomaster

1. anonymous

2. anonymous

well... find the one-sided limits for the piece-wise function if the $$\bf \lim\limits_{x\to 0^-}\textit{ is equal to }\lim\limits_{x\to 0^+} \\ \quad \\ then\qquad \lim\limits_{x\to 0}\ exist$$

3. anonymous

$$\large \lim\limits_{x\to 0}\qquad \begin{cases} 7-x^2&x<0\quad \textit{left side, thus } \lim\limits_{x\to 0^-}\\ 7&x=0\\ 10x+7&x>0\quad \textit{right side, thus } \lim\limits_{x\to 0^+} \end{cases}$$ that is, if the left-side of the "limit" matches the right-side of the "limit" in this case those 2 equations, (notice the limit occurs when "x" approaches 0) then the double-sided limit exist and is THAT

4. anonymous

very simple if you simply set x = 0 for those equations btw

5. anonymous

i dont get it @jdoe0001 can u help me step by step?

6. anonymous

so would the answer be 7? @jdoe0001

7. anonymous

.. how did you get 7 though?

8. anonymous

i set replaced x with 0 @jdoe0001

9. anonymous

am i right or wrong? @jdoe0001

10. anonymous

well... is a piece-wise, so there are 3 equations there.. so... which one did you set to 0?

11. anonymous

all of them @jdoe0001

12. anonymous

am i wrong is the answer not 7? @jdoe0001

13. anonymous

$$\bf \lim\limits_{x\to 0^-}\quad 7-x^2=?\impliedby \textit{left side limit} \\ \quad \\ \lim\limits_{x\to 0^+}\quad 10x+7=?\impliedby \textit{right side limit}$$ say... what would you get for those two?

14. anonymous

i would get 7 @jdoe0001

15. anonymous

ok... so, the left-sided limit gives 7 the right-sided limit gives 7 then $$\bf \lim\limits_{x\to 0} \implies 7$$ :)

16. anonymous

can u help me with another? @jdoe0001

17. anonymous

sure, post anew, more eyes :)

18. anonymous

thus if I dunno, someone else may help