Analytic Geometry With Introductory Chapter On the Calculus
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In our eReader you can find the full English version of the book. Read Analytic Geometry With Introductory Chapter On the 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 Analytic Geometry With Introductory Chapter On the Calculus
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To quickly assess the difficulty of the text, read a short excerpt:
For d(e u + C) = e u du.
/Vdu = ^ + c.
log a For d(r^- + 6] = a u du. Moe a I By XXV. By XXIV.
203] ELEMENTS OF CALCULUS 259 Example. Find the area bounded by the equilateral hyperbola xy = 4, the z-axis, and the ordinates corresponding to x = 1 and x = 8.
Solution. The hyperbola is shown in Fig. 170, and the area sought is MNQR.
Consider the area A as generated by the ordinate moving toward the right.
Then dA = ydx.
And fdA = fydx = f-dx = 4 f^- / x / x A = 4 log x + C.
When x = 1, A = 0. . * .... = 4 log 1 + C, or C = -4 log 1. When x = 8, A = 4 log 8 - 4 log 1.
A = 4 X 2. 079 -4X0= 8. 316. Therefore the area sought is 8. 316 square units.
EXERCISES In exercises 1-20 find the derivatives of the dependent variables with respect to the independent variables, and the differentials of the dependent variables.
1. Y = log (x 2 + 7x). 1. Y = e* x * + *.
2. Y = logic x 2 . 8. Y = e x sin x.
3. Y = log - 9. Y = a 2x .
4. Y = l oglo or 2 . 10. Y = x-W 2x+3 . 6. Y = e 2x . 11. Y = (3x - 2)*. 6. Y = e x \ 12.
What to read after Analytic Geometry With Introductory Chapter On the Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Claude Irwin Palmer to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
For d(e u + C) = e u du.
/Vdu = ^ + c.
log a For d(r^- + 6] = a u du. Moe a I By XXV. By XXIV.
203] ELEMENTS OF CALCULUS 259 Example. Find the area bounded by the equilateral hyperbola xy = 4, the z-axis, and the ordinates corresponding to x = 1 and x = 8.
Solution. The hyperbola is shown in Fig. 170, and the area sought is MNQR.
Consider the area A as generated by the ordinate moving toward the right.
Then dA = ydx.
And fdA = fydx = f-dx = 4 f^- / x / x A = 4 log x + C.
When x = 1, A = 0. . * .... = 4 log 1 + C, or C = -4 log 1. When x = 8, A = 4 log 8 - 4 log 1.
A = 4 X 2. 079 -4X0= 8. 316. Therefore the area sought is 8. 316 square units.
EXERCISES In exercises 1-20 find the derivatives of the dependent variables with respect to the independent variables, and the differentials of the dependent variables.
1. Y = log (x 2 + 7x). 1. Y = e* x * + *.
2. Y = logic x 2 . 8. Y = e x sin x.
3. Y = log - 9. Y = a 2x .
4. Y = l oglo or 2 . 10. Y = x-W 2x+3 . 6. Y = e 2x . 11. Y = (3x - 2)*. 6. Y = e x \ 12.
What to read after Analytic Geometry With Introductory Chapter On the Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Claude Irwin Palmer to read onlineMoreLess
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