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What does it mean by measures the arc length? Suppose that the function f(x, y) is defined throughout a region R in the xy-plane, that Palxo vol is a point in R. and that u itwi is a unit vector Then the equations

What does it mean by measures the arc length? Suppose that the function f(x, y) is defined throughout a region R in the xy-plane, that Palxo vol is a point in R. and that u itwi is a unit vector Then the equations

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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What does it mean by measures the arc length? Suppose that the function f(x, y) is defined throughout a region R in the xy-plane, that Po(xo, yo) is a point in R, and that u = u₁i + u₂j is a unit vector. Then the equations x = xo + su₁, y = yo + su₂ parametrize the line through Po parallel to u. If the parameter s measures arc length from Po in the direction of u, we find the rate of change of f at Po in the direction of u by calcu- lating df/ds at Po (Figure 14.27). 4 DEFINITION The derivative of f at Po(xo, Yo) in the direction of the unit vector u = u₁i + u₂j is the number df ds = lim 3-0 u. Po provided the limit exists. - f(xo + su₁, Yo + su₂) = f(xo, Yo) S (1)
Transcribed Image Text:What does it mean by measures the arc length? Suppose that the function f(x, y) is defined throughout a region R in the xy-plane, that Po(xo, yo) is a point in R, and that u = u₁i + u₂j is a unit vector. Then the equations x = xo + su₁, y = yo + su₂ parametrize the line through Po parallel to u. If the parameter s measures arc length from Po in the direction of u, we find the rate of change of f at Po in the direction of u by calcu- lating df/ds at Po (Figure 14.27). 4 DEFINITION The derivative of f at Po(xo, Yo) in the direction of the unit vector u = u₁i + u₂j is the number df ds = lim 3-0 u. Po provided the limit exists. - f(xo + su₁, Yo + su₂) = f(xo, Yo) S (1)
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