Calculus
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In our eReader you can find the full English version of the book. Read Calculus 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 Calculus
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The length of arc AB is defined by g = lim y Ac, 1 P Q ^1 b- • Fig. 49.
where Ac is the length of the chord PQ. Then ='^s.%^huE)'^- Since 1.
it follows by Duhamel's Theorem that b -."zSaKIT'^- 112 CALCULUS [§70 Hence, =r^^^^^- Exercises 1. Find the length of the curve y = x' between the points (0, 0) and (1, 1).
3 2 2 2. Find the entire length oi x' + y^ = a'- 3. Find the entire length of x' + j/' = a'.
4. Find the length of y' = 4x' between the points (0, 0) and (4, 16).
70. Area of a Surface... of Revolution. The portion AB, Fig. 49, of the curve y = f{x), between the ordinates a; = o and x = b, is revolved about the X-axis. Find the area, S, of the surface generated.
Pass planes as in §69 perpendicular to the Z-axis tlrfough the equidistant points of division of the interval CH = b — a.
Denote the convex surface of the frustum of the cone generated by the revolution of DEPQ by AF. The area, S, of the surface of re- volution will be defined as the limit of the sum of the convex surfaces, AF, of these frusta as n becomes infinite, i.e., as Ax approaches zero.
What to read after Calculus?
You can find similar books in the "Read Also" column, or choose other free books by March, Herman W. (Herman William), B. 1878 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The length of arc AB is defined by g = lim y Ac, 1 P Q ^1 b- • Fig. 49.
where Ac is the length of the chord PQ. Then ='^s.%^huE)'^- Since 1.
it follows by Duhamel's Theorem that b -."zSaKIT'^- 112 CALCULUS [§70 Hence, =r^^^^^- Exercises 1. Find the length of the curve y = x' between the points (0, 0) and (1, 1).
3 2 2 2. Find the entire length oi x' + y^ = a'- 3. Find the entire length of x' + j/' = a'.
4. Find the length of y' = 4x' between the points (0, 0) and (4, 16).
70. Area of a Surface... of Revolution. The portion AB, Fig. 49, of the curve y = f{x), between the ordinates a; = o and x = b, is revolved about the X-axis. Find the area, S, of the surface generated.
Pass planes as in §69 perpendicular to the Z-axis tlrfough the equidistant points of division of the interval CH = b — a.
Denote the convex surface of the frustum of the cone generated by the revolution of DEPQ by AF. The area, S, of the surface of re- volution will be defined as the limit of the sum of the convex surfaces, AF, of these frusta as n becomes infinite, i.e., as Ax approaches zero.
What to read after Calculus?
You can find similar books in the "Read Also" column, or choose other free books by March, Herman W. (Herman William), B. 1878 to read onlineMoreLess
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