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Write down an expression for the area of each region described by the following

Mathematics for the International Student: Mathematics SL | 3rd Edition | ISBN: 9781921972089 | Authors: Sandra Haese, Michael Haese, Robert Haese, Mark Humphries, Marjut Maenpaa ISBN: 9781921972089 446

Solution for problem 4 Chapter 19

Mathematics for the International Student: Mathematics SL | 3rd Edition

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Mathematics for the International Student: Mathematics SL | 3rd Edition | ISBN: 9781921972089 | Authors: Sandra Haese, Michael Haese, Robert Haese, Mark Humphries, Marjut Maenpaa

Mathematics for the International Student: Mathematics SL | 3rd Edition

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Problem 4

Write down an expression for the area of each region described by the following boundaries. Use technology to calculate the area. a y = ln x, the x-axis, x = 1, and x = 4 b y = x sin x, the x-axis, x = 1, and x = 2 c y = x2ex, the x-axis, x = 0, and x = 2:8 .

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Spencer Kociba MATH 200-005 Lecture Notes Week 6 10/24/2016 Directional Derivatives ● Definition for Directional Derivatives ○ If f(x,y) is a function and u =< u ,u > is a unit vector, then the directonal 1 2 derivative of f in the direction of u at (x ,y ) is denoted D f(x ,y ) and is given o o u o o by D f(x ,y ) = d [f(x + u s, y + u s)]|s = 0 u o o ds o 1 o 2 ○ D f(x ,y ) = lim f(o +1 ho y2+u ho−o(x ,y ) u o o h→0 h ● Notes ○ fx(o ,yo) = Duf(xo,yo) u=<1,0> ○ fy(o ,yo) = Duf(xo,yo) u=<0,1> ○ If u is a unit vector < u 1u ,2 >3, then D u(xo,y oz o = d[f(xo+ u 1, y o u 2,z o u s3|s = 0 ds ● Theorem ○ If f(x,y) is differentiable at (xo,yo) and u =< u ,1 > 2s a unit vector then D u(xo,y o exists and D f(u ,yo) o f (xx,yo)uo+ 1 (x yyo)u o 2 Spencer Kociba MATH 200-005 Lecture Notes Week 6 10/25/2016 Directional Derivatives ● D u(x oy o = f xxo,y ou 1 f yx oy ou 2 ● Definition of gradient ○ If f is a function of x and y, the gradient of f is defined by ∇f(x,y) = < f xx,y),f yx,y) > ○ Similarly, ∇f(x,y,z) = < f (xxy,z),f (xyy,z),f (xzy,z) > ● Note:

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Chapter 19, Problem 4 is Solved
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Textbook: Mathematics for the International Student: Mathematics SL
Edition: 3
Author: Sandra Haese, Michael Haese, Robert Haese, Mark Humphries, Marjut Maenpaa
ISBN: 9781921972089

Since the solution to 4 from 19 chapter was answered, more than 243 students have viewed the full step-by-step answer. Mathematics for the International Student: Mathematics SL was written by and is associated to the ISBN: 9781921972089. This full solution covers the following key subjects: . This expansive textbook survival guide covers 25 chapters, and 453 solutions. The answer to “Write down an expression for the area of each region described by the following boundaries. Use technology to calculate the area. a y = ln x, the x-axis, x = 1, and x = 4 b y = x sin x, the x-axis, x = 1, and x = 2 c y = x2ex, the x-axis, x = 0, and x = 2:8 .” is broken down into a number of easy to follow steps, and 64 words. This textbook survival guide was created for the textbook: Mathematics for the International Student: Mathematics SL, edition: 3. The full step-by-step solution to problem: 4 from chapter: 19 was answered by , our top Math solution expert on 03/15/18, 06:04PM.

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Write down an expression for the area of each region described by the following