math456
Need help! Explain why the function is discontinuous at the given number a. Sketch the graph of the function!



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math456
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math456
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@cwrw238 @Hero

math456
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@jim_thompson5910

jim_thompson5910
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what is cos(0)

math456
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its 1

jim_thompson5910
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so notice how in the first piece, the y value at x = 0 is 1
but the y value in the second piece at x = 0 is 0
Can you visualize what I'm describing?

math456
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yea so that means \[\cos x \neq x=0\]

jim_thompson5910
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do you mean cos(x) doesn't equal x when x = 0?

math456
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yea because at x its 0 and at x<0 its 1

jim_thompson5910
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then you are correct, and this shows us that there is a discontinuity

math456
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alright kool thanks and does the graph looks like this?dw:1348180882506:dw

jim_thompson5910
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you're on the right track

jim_thompson5910
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however, you only graph cos(x) when x < 0

jim_thompson5910
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and you only graph 1  x^2 when x > 0

jim_thompson5910
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make sure you draw a hole at (0,1) and a closed circle at (0,0)

math456
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dw:1348181069990:dw like this?

jim_thompson5910
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closer, but now erase the piece of cos(x) that's to the right of x = 0
and erase the piece of 1  x^2 that's to the left of x = 0

math456
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dw:1348181225073:dw

jim_thompson5910
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good, you got it

math456
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alright thanks for ur help!
