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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2So you need your answer checked? Or you also need an explanation?

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0i accidentally checked the first one. an explanatoion would be great@

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2have you learned about left hand limits? and right hand limits?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2so you know what this notation means? \[\LARGE \lim_{x \to 1^{}} f(x)\]

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0yes the limit is approaching 1 from the left side

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2which piece will be used here? the x^2 + 4 piece? or the x+4 piece?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yes because f(x) = x^2 + 4 if x < 1

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2so 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
 one year ago
Best ResponseYou've already chosen the best response.0so it would be c because it doesn't equal 1?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2well let's compute the right hand limit

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2do you know how to do so?

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0The limit as x approaches 1 from the right side and plus in x=1 into x+4 ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yes because f(x) = x+4 when x > 1

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0It also = 5 from the right side

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yes, \[\LARGE \lim_{x \to 1^{+}} f(x) = 5\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2because 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
 one year ago
Best ResponseYou've already chosen the best response.0so then it would be continuous

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2actually wait...f(1) isn't defined

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2I'm not thinking

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2the piecewise function is set up in a way where x = 1 is left out

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2notice how there are NO underlines under the > or the <

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Ohh i didnt notice that either

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2f(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
 one year ago
Best ResponseYou've already chosen the best response.0Okay, thank you for explaing this problem i appreciate it!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2you're welcome
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