I think you could do it like this:
Let f(x) be the odd function we’re gonna work with. So, f(-x) = -f(x), By the definition of the derivative:
f'(x) = ##lim_(h->0)(f(x+h) – f(x))/h##.
We want to prove that f'(-x) = f'(x). Now, f'(-x) is:
##f'(-x) = lim_(h->0)(f(-x+h)-f(-x))/h## .
Since f(x) is and odd function, f(-x) = -f(x), therefore, we can rewrite the above expression as:
##f'(-x) = lim_(h->0)((-f(x-h)) + f(x))/h## = ##lim_(h->0)[-(f(x-h)-f(x))/h]##.
But we can rewrite the above expression as:
##f'(-x) = lim_(h->0)(f(x-h)-f(x))/-h##.
To make things clearer, let t = -h. Therefore:
##f'(-x) = lim_(t->0)(f(x+t)-f(x))/t##, which is just f'(x). That is: f'(-x) = f'(x). And there we have it: if f(x) is an odd function, then f'(x) is an even function.
Hope it helps you!
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How Do You Measure Political Influence What Are The Advantages And Disadvantages
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• Do you generally employ a more positional or interest-based approach to conflict management (see pp. 7 and 8 of your textbook)?
• Please compare and contrast your personal response with that of your professional response. If there’s a difference between the two, in what way do you behave differently and what do you feel is the explanation for this behaviour?
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Clearly read –
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Require Turnirin report
No plagiarism
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Stakeholderanalysis in conflictresolution, projectmanagement,and businessadministration, is the process of identifying the individuals or groups that are likely to affector be affected by a…
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How Do You Prove That 1 2 Ln2 Ln4 Ln3 1 2 Ln 3 2
/in Uncategorized /by developerIn the bracket with ##(ln2-ln4+ln3)## you can apply the following general rules of the logarithms:
1) ##lna+lnb=ln(a*b)##
2) ##lna-lnb=ln(a/b)##
and you should be able to get your result.
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How Do You Put This In Standard Form And Diagram It
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It is time we brought our troops home from South Korea. The 40,000 GIs stationed in South Korea support a corrupt regime. The savings in dollars which would result from their coming home would make a sizeable dent in the federal deficit. Furthermore, the Korean conflict ended over 30 years ago.
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‘ ‘ ‘u. ,Eu’.{‘-n.’..1.-.:~.- 43:3.«tuna: 3:45, :12”: 3:1,:th J’H’W 15 r ’1 " W wawcetm adem ‘06H4 and“ why;0660“"? Wm WM germ/60M. w . 3 . ,pdanpmcne 4 . A 3 W {ama…
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Future of Advocacy on National level• All the National governments will fulfil their responsibility for formulating andimplementing national policy honestly. Rights are equal for all. •…
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Sheet1 InvestmentL InvestmentInterestConstraints:Total fundsLow IncomeConvenitionalGovermentBondStockFuturesNon-MortageHigh-YeildMax Allowed CGBSCONVENITIONALOW INCOMEL…
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How Do You Show That The Derivative Of An Odd Function Is Even
/in Uncategorized /by developerI think you could do it like this:
Let f(x) be the odd function we’re gonna work with. So, f(-x) = -f(x), By the definition of the derivative:
f'(x) = ##lim_(h->0)(f(x+h) – f(x))/h##.
We want to prove that f'(-x) = f'(x). Now, f'(-x) is:
##f'(-x) = lim_(h->0)(f(-x+h)-f(-x))/h## .
Since f(x) is and odd function, f(-x) = -f(x), therefore, we can rewrite the above expression as:
##f'(-x) = lim_(h->0)((-f(x-h)) + f(x))/h## = ##lim_(h->0)[-(f(x-h)-f(x))/h]##.
But we can rewrite the above expression as:
##f'(-x) = lim_(h->0)(f(x-h)-f(x))/-h##.
To make things clearer, let t = -h. Therefore:
##f'(-x) = lim_(t->0)(f(x+t)-f(x))/t##, which is just f'(x). That is: f'(-x) = f'(x). And there we have it: if f(x) is an odd function, then f'(x) is an even function.
Hope it helps you!
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