http://prntscr.com/88wnz4 ap calc ab

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http://prntscr.com/88wnz4 ap calc ab

Mathematics
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So you need your answer checked? Or you also need an explanation?
i accidentally checked the first one. an explanatoion would be great@
have you learned about left hand limits? and right hand limits?

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Other answers:

yes
so you know what this notation means? \[\LARGE \lim_{x \to 1^{-}} f(x)\]
yes the limit is approaching 1 from the left side
correct
which piece will be used here? the x^2 + 4 piece? or the x+4 piece?
x^2+4
yes because f(x) = x^2 + 4 if x < 1
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, \[\LARGE \lim_{x \to 1^{-}} f(x) = 5\]
so it would be c because it doesn't equal 1?
well let's compute the right hand limit
do you know how to do so?
The limit as x approaches 1 from the right side and plus in x=1 into x+4 ?
yes because f(x) = x+4 when x > 1
plug in*
ok ill try it
It also = 5 from the right side
yes, \[\LARGE \lim_{x \to 1^{+}} f(x) = 5\]
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.
so then it would be continuous
actually wait...f(1) isn't defined
I'm not thinking
the piecewise function is set up in a way where x = 1 is left out
notice how there are NO underlines under the > or the <
Ohh i didnt notice that either
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
Okay, thank you for explaing this problem i appreciate it!
you're welcome

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