Lectures On the Theory of Functions of Real Variables 1
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In our eReader you can find the full English version of the book. Read Lectures On the Theory of Functions of Real Variables 1 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 Lectures On the Theory of Functions of Real Variables 1
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To quickly assess the difficulty of the text, read a short excerpt:
w — 1 ! nl where A is independent of u. This function is obviously a con- tinuous function of u in 21 for any x in St. Differentiating with respect to u, we get, observing terms cancel in pairs, 9'(u:, = (^^ZJDTI s -/")(^) + AI (3 71—11 for any u tvithin 21.
Thus the derivative of g{u') is finite within 21.
To apply Rolle's theorem to g(u)-, with reference to the interval ^ = (a, a;), it is only necessary to determine A in 2) so that But obviously g(x')=0.
We therefore suppose A so chosen that ...=f(x-) -fCa-) -(x- a)f\a^ - •.• - -fcl^)^/(-i)(«) - (^z:^ A. (4 w— 1 ! w 1 Then by Rolle's theorem, there is a point a(c)-^l = 0. (5 M— 1 1 As c^^a;, the first factor in 5) is not 0. Hence the parenthesis is 0, which gives r^\c)=A.
Putting this value of A in 4), we have 1).
TAYLOR'S DEVELOPMENT IN FINITE FORM 257 2. The formula 1) is called Taylor s development of f(cc) in finite form.
It may also be written as follows : Set x = a+h, c = a-\-6h.
What to read after Lectures On the Theory of Functions of Real Variables 1?
You can find similar books in the "Read Also" column, or choose other free books by James Pierpont to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
w — 1 ! nl where A is independent of u. This function is obviously a con- tinuous function of u in 21 for any x in St. Differentiating with respect to u, we get, observing terms cancel in pairs, 9'(u:, = (^^ZJDTI s -/")(^) + AI (3 71—11 for any u tvithin 21.
Thus the derivative of g{u') is finite within 21.
To apply Rolle's theorem to g(u)-, with reference to the interval ^ = (a, a;), it is only necessary to determine A in 2) so that But obviously g(x')=0.
We therefore suppose A so chosen that ...=f(x-) -fCa-) -(x- a)f\a^ - •.• - -fcl^)^/(-i)(«) - (^z:^ A. (4 w— 1 ! w 1 Then by Rolle's theorem, there is a point a
Putting this value of A in 4), we have 1).
TAYLOR'S DEVELOPMENT IN FINITE FORM 257 2. The formula 1) is called Taylor s development of f(cc) in finite form.
It may also be written as follows : Set x = a+h, c = a-\-6h.
What to read after Lectures On the Theory of Functions of Real Variables 1?
You can find similar books in the "Read Also" column, or choose other free books by James Pierpont to read onlineMoreLess
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