Problems in the Calculus, With Formulas And Suggestions
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In our eReader you can find the full English version of the book. Read Problems in the Calculus, With Formulas And Suggestions 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 Problems in the Calculus, With Formulas And Suggestions
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21. (9 + x)i 23. (16 - x)*. 25. (16 + s)*.
EXERCISE LVI Expansion in Powers of (x — a). Taylor's Theorem. It is some- times very desirable to have a function expanded in powers of (x — a), where a is some constant. This is accomplished by Taylor's theorem, F"(d] F'"(a) F(x)=F(a)+F>(a)(x- a )+ -±l(x-af+ —U.(x-af+. . . .
That is, the successive coefficients are simply the successive derivatives of F(x), evaluated for x = a. The series may be 80 PROBLEMS IN THE CALCULUS finite or infinite. Observe... that a may be a positive or negative quantity. Expand the following in terms of the quantities indicated.
1. tana; in powers of (x — ■jt/4) ; of (x + 7r/4) ; of (x + 2).
2. sinx in powers of (x - tt/3) ; of (x + tt/6) ; of (x — tt/4).
3. x* — 3 x 3 — x 2 — 5 x — 11 in powers of (x — 2).
4. x 4 — 5x 2 + 8x — 7 in powers of (x + 1) ; of (x — 2).
5. x 6 — 2x 8 + 4x in powers of (x + 1).
6. & in powers of (x + 3). 11. cos 3 x in powers of (x — ir/6).
7. e Sx in powers of (x — 4).
What to read after Problems in the Calculus, With Formulas And Suggestions?
You can find similar books in the "Read Also" column, or choose other free books by Leib, David D. (David Deitch), 1879- to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
21. (9 + x)i 23. (16 - x)*. 25. (16 + s)*.
EXERCISE LVI Expansion in Powers of (x — a). Taylor's Theorem. It is some- times very desirable to have a function expanded in powers of (x — a), where a is some constant. This is accomplished by Taylor's theorem, F"(d] F'"(a) F(x)=F(a)+F>(a)(x- a )+ -±l(x-af+ —U.(x-af+. . . .
That is, the successive coefficients are simply the successive derivatives of F(x), evaluated for x = a. The series may be 80 PROBLEMS IN THE CALCULUS finite or infinite. Observe... that a may be a positive or negative quantity. Expand the following in terms of the quantities indicated.
1. tana; in powers of (x — ■jt/4) ; of (x + 7r/4) ; of (x + 2).
2. sinx in powers of (x - tt/3) ; of (x + tt/6) ; of (x — tt/4).
3. x* — 3 x 3 — x 2 — 5 x — 11 in powers of (x — 2).
4. x 4 — 5x 2 + 8x — 7 in powers of (x + 1) ; of (x — 2).
5. x 6 — 2x 8 + 4x in powers of (x + 1).
6. & in powers of (x + 3). 11. cos 3 x in powers of (x — ir/6).
7. e Sx in powers of (x — 4).
What to read after Problems in the Calculus, With Formulas And Suggestions?
You can find similar books in the "Read Also" column, or choose other free books by Leib, David D. (David Deitch), 1879- to read onlineMoreLess
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