Elements of the Differential And Integral Calculus With Examples And Applications
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In our eReader you can find the full English version of the book. Read Elements of the Differential And Integral Calculus With Examples And Applications Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Elements of the Differential And Integral Calculus With Examples And Applications
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To quickly assess the difficulty of the text, read a short excerpt:
Any value of x which renders fx a maximum or a Tninimum is a root of f x = 0?" f x = cp.
From § 101 it follows that/'x changes its quality when/x passes through either a maximum or a minimum.
When fx is continuous for all values of x, fx must pass through zero to change its quality.
When fx is a fraction whose denominator becomes zero for some finite value of x, fx may change its quality by becoming cp.
For example, when s — 2 = 0orx = 2, the fraction a/ (x — 2) becomes ap and changes its quali...ty. Again, tan x, or sin a; /cos x, becomes ap and changes its quality when cos x = 0, or x = ;r/2.
MAXIMA AND MINIMA.
83 The converse of this theorem is not true ; that is, any root oif'x = or f'x = ap does not necessarily render fx either a maximum or a minimum. These roots are simply the critical values of x, for each of which the function is to be examined.
103. Geometric illustration.
Let adefh be the locus of y =fx.
Then /x will be represented by the ordinate of the point {», y), and /'a by the slope of the locus at the point (s, y).
What to read after Elements of the Differential And Integral Calculus With Examples And Applications?
You can find similar books in the "Read Also" column, or choose other free books by James M James Morford Taylor to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Any value of x which renders fx a maximum or a Tninimum is a root of f x = 0?" f x = cp.
From § 101 it follows that/'x changes its quality when/x passes through either a maximum or a minimum.
When fx is continuous for all values of x, fx must pass through zero to change its quality.
When fx is a fraction whose denominator becomes zero for some finite value of x, fx may change its quality by becoming cp.
For example, when s — 2 = 0orx = 2, the fraction a/ (x — 2) becomes ap and changes its quali...ty. Again, tan x, or sin a; /cos x, becomes ap and changes its quality when cos x = 0, or x = ;r/2.
MAXIMA AND MINIMA.
83 The converse of this theorem is not true ; that is, any root oif'x = or f'x = ap does not necessarily render fx either a maximum or a minimum. These roots are simply the critical values of x, for each of which the function is to be examined.
103. Geometric illustration.
Let adefh be the locus of y =fx.
Then /x will be represented by the ordinate of the point {», y), and /'a by the slope of the locus at the point (s, y).
What to read after Elements of the Differential And Integral Calculus With Examples And Applications?
You can find similar books in the "Read Also" column, or choose other free books by James M James Morford Taylor to read onlineMoreLess
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