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C3 Edexcel Do I state Change of Sign AND continuous??

when doing numerical methods questions there is often a part that wants you to prove that there's a root at a particular x-value. To do this I know I have to find the change of sign in y-values for an interval between that x-value and then state that because there is a change in sign AND F(X) IS CONTINUOUS, there is a root at that x-value. My issue is not knowing how f(x) is continuous, and whether saying its continuous applies to all such questions? Any help would be much appreciated.
Original post by lordoftheties
when doing numerical methods questions there is often a part that wants you to prove that there's a root at a particular x-value. To do this I know I have to find the change of sign in y-values for an interval between that x-value and then state that because there is a change in sign AND F(X) IS CONTINUOUS, there is a root at that x-value. My issue is not knowing how f(x) is continuous, and whether saying its continuous applies to all such questions? Any help would be much appreciated.


Just substitute the x value in. If it's a root you get 0.
Original post by morgan8002
Just substitute the x value in. If it's a root you get 0.


That's the other type of question. Im referring to this kind (part c):Screen Shot 2016-05-03 at 13.19.49.png
Original post by lordoftheties
That's the other type of question. Im referring to this kind (part c):Screen Shot 2016-05-03 at 13.19.49.png


Yes, you'd need to state continuity. Exponentials, sines, cosines, constant functions and polynomials are all continuous. Also, finitely adding, multiplying or composing continuous functions gives a continuous function so g(x) is continuous.
Yes just always say "sign change, therefore root in the interval, given that f(x) is continuous"
Original post by 雷尼克
Yes just always say "sign change, therefore root in the interval, given that f(x) is continuous"


Im not sure if youre ALWAYS supposed to say continuous, the bold section of this part of the mark scheme for that question says something about not stating continuous...Screen Shot 2016-05-03 at 14.10.12.png
Original post by lordoftheties
Im not sure if youre ALWAYS supposed to say continuous, the bold section of this part of the mark scheme for that question says something about not stating continuous...Screen Shot 2016-05-03 at 14.10.12.png


That has nothing to do with 'continuous'... that part of the marking scheme is telling the examiner that it is an invalid method to continue the iterations.
Original post by lordoftheties
Im not sure if youre ALWAYS supposed to say continuous, the bold section of this part of the mark scheme for that question says something about not stating continuous...Screen Shot 2016-05-03 at 14.10.12.png


It's not talking about continuity. It's talking about substituting repeatedly into the difference equation from (b) to find bounds on α\alpha.
Original post by morgan8002
It's not talking about continuity. It's talking about substituting repeatedly into the difference equation from (b) to find bounds on α\alpha.


Oh I see now. Thanks a lot guys.
Original post by lordoftheties
when doing numerical methods questions there is often a part that wants you to prove that there's a root at a particular x-value. To do this I know I have to find the change of sign in y-values for an interval between that x-value and then state that because there is a change in sign AND F(X) IS CONTINUOUS, there is a root at that x-value. My issue is not knowing how f(x) is continuous, and whether saying its continuous applies to all such questions? Any help would be much appreciated.


The function does have to be contiuous for this logic to work, but Edexcel don't expect you to say it.

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