Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 3, Problem 57SP
To determine
The paper on history of Fermat’s Last theorem.
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(a) Use differentiation to find a power series representation for
1
f(x)
=
(4 + x)²*
f(x)
=
00
Σ
n = 0
What is the radius of convergence, R?
R =
(b) Use part (a) to find a power series for
f(x)
=
1
(4 + x)³°
f(x) =
00
Σ
n = 0
What is the radius of convergence, R?
R =
(c) Use part (b) to find a power series for
f(x)
=
x²
(4 + x)³*
00
f(x) = Σ
n = 2
What is the radius of convergence, R?
R =
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answer for question 4 please
(3) (20 points) Let F(x, y, z) = (y, z, x²z). Define
E = {(x, y, z) | x² + y² ≤ z ≤ 1, x ≤ 0}.
(a) (2 points) Calculate the divergence V. F.
(b) (4 points) Let D = {(x, y) | x² + y² ≤ 1, x ≤ 0} Without calculation, show that
the triple integral
√ (V · F) dV = √ 2²(1.
= x²(1 − x² - y²) dA.
E
Chapter 3 Solutions
Calculus
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- (2) (22 points) Let F(x, y, z) = (x sin y, cos y, ―xy). (a) (2 points) Calculate V. F. (b) (6 points) Given a vector field is everywhere defined with V G₁(x, y, z) = * G2(x, y, z) = − G3(x, y, z) = 0. 0 0 F(x, y, z) = (F₁(x, y, z), F₂(x, y, z), F(x, y, z)) that F = 0, let G = (G1, G2, G3) where F₂(x, y, y, t) dt - √ F³(x, t, 0) dt, * F1(x, y, t) dt, t) dt - √ F Calculate G for the vector field F(x, y, z) = (x sin y, cos y, -xy).arrow_forwardEvaluate the following integral over the Region R. (Answer accurate to 2 decimal places). √ √(x + y) A R R = {(x, y) | 25 < x² + y² ≤ 36, x < 0} Hint: The integral and Region is defined in rectangular coordinates.arrow_forwardFind the volume of the solid that lies under the paraboloid z = 81 - x² - y² and within the cylinder (x − 1)² + y² = 1. A plot of an example of a similar solid is shown below. (Answer accurate to 2 decimal places). Volume using Double Integral Paraboloid & Cylinder -3 Hint: The integral and region is defined in polar coordinates.arrow_forward
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