tmagloire1
  • tmagloire1
http://prntscr.com/88wnz4 ap calc ab
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
jim_thompson5910
  • jim_thompson5910
So you need your answer checked? Or you also need an explanation?
tmagloire1
  • tmagloire1
i accidentally checked the first one. an explanatoion would be great@
jim_thompson5910
  • jim_thompson5910
have you learned about left hand limits? and right hand limits?

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tmagloire1
  • tmagloire1
yes
jim_thompson5910
  • jim_thompson5910
so you know what this notation means? \[\LARGE \lim_{x \to 1^{-}} f(x)\]
tmagloire1
  • tmagloire1
yes the limit is approaching 1 from the left side
jim_thompson5910
  • jim_thompson5910
correct
jim_thompson5910
  • jim_thompson5910
which piece will be used here? the x^2 + 4 piece? or the x+4 piece?
tmagloire1
  • tmagloire1
x^2+4
jim_thompson5910
  • jim_thompson5910
yes because f(x) = x^2 + 4 if x < 1
jim_thompson5910
  • 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, \[\LARGE \lim_{x \to 1^{-}} f(x) = 5\]
tmagloire1
  • tmagloire1
so it would be c because it doesn't equal 1?
jim_thompson5910
  • jim_thompson5910
well let's compute the right hand limit
jim_thompson5910
  • jim_thompson5910
do you know how to do so?
tmagloire1
  • tmagloire1
The limit as x approaches 1 from the right side and plus in x=1 into x+4 ?
jim_thompson5910
  • jim_thompson5910
yes because f(x) = x+4 when x > 1
tmagloire1
  • tmagloire1
plug in*
tmagloire1
  • tmagloire1
ok ill try it
tmagloire1
  • tmagloire1
It also = 5 from the right side
jim_thompson5910
  • jim_thompson5910
yes, \[\LARGE \lim_{x \to 1^{+}} f(x) = 5\]
jim_thompson5910
  • 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.
tmagloire1
  • tmagloire1
so then it would be continuous
jim_thompson5910
  • jim_thompson5910
actually wait...f(1) isn't defined
jim_thompson5910
  • jim_thompson5910
I'm not thinking
jim_thompson5910
  • jim_thompson5910
the piecewise function is set up in a way where x = 1 is left out
jim_thompson5910
  • jim_thompson5910
notice how there are NO underlines under the > or the <
tmagloire1
  • tmagloire1
Ohh i didnt notice that either
jim_thompson5910
  • 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
tmagloire1
  • tmagloire1
Okay, thank you for explaing this problem i appreciate it!
jim_thompson5910
  • jim_thompson5910
you're welcome

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