## tmagloire1 one year ago http://prntscr.com/88wnz4 ap calc ab

1. jim_thompson5910

So you need your answer checked? Or you also need an explanation?

2. tmagloire1

i accidentally checked the first one. an explanatoion would be great@

3. jim_thompson5910

have you learned about left hand limits? and right hand limits?

4. tmagloire1

yes

5. jim_thompson5910

so you know what this notation means? $\LARGE \lim_{x \to 1^{-}} f(x)$

6. tmagloire1

yes the limit is approaching 1 from the left side

7. jim_thompson5910

correct

8. jim_thompson5910

which piece will be used here? the x^2 + 4 piece? or the x+4 piece?

9. tmagloire1

x^2+4

10. jim_thompson5910

yes because f(x) = x^2 + 4 if x < 1

11. jim_thompson5910

so what we do is simply plug in x = 1 to get f(1) = 1^2 + 4 = 1+4 = 5 as x gets closer and closer to 1 from the left side, the limiting value is 5 in other words, $\LARGE \lim_{x \to 1^{-}} f(x) = 5$

12. tmagloire1

so it would be c because it doesn't equal 1?

13. jim_thompson5910

well let's compute the right hand limit

14. jim_thompson5910

do you know how to do so?

15. tmagloire1

The limit as x approaches 1 from the right side and plus in x=1 into x+4 ?

16. jim_thompson5910

yes because f(x) = x+4 when x > 1

17. tmagloire1

plug in*

18. tmagloire1

ok ill try it

19. tmagloire1

It also = 5 from the right side

20. jim_thompson5910

yes, $\LARGE \lim_{x \to 1^{+}} f(x) = 5$

21. jim_thompson5910

because f(1) is defined, and because the left and right hand limits equal the same value, this means f(x) is continuous at x = 1. It's continuous everywhere else because the two pieces are polynomials. All polynomials are continuous.

22. tmagloire1

so then it would be continuous

23. jim_thompson5910

actually wait...f(1) isn't defined

24. jim_thompson5910

I'm not thinking

25. jim_thompson5910

the piecewise function is set up in a way where x = 1 is left out

26. jim_thompson5910

notice how there are NO underlines under the > or the <

27. tmagloire1

Ohh i didnt notice that either

28. jim_thompson5910

f(x) = x^2 + 4 if x < 1 OR f(x) = x + 4 if x > 1 but what if x = 1 ? The function doesn't say, so f(1) is undefined

29. tmagloire1

Okay, thank you for explaing this problem i appreciate it!

30. jim_thompson5910

you're welcome

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