University Calculus: Early Transcendentals, Books a la Carte Edition (3rd Edition)
3rd Edition
ISBN: 9780321999610
Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Chapter A.2, Problem 7E
To determine
Show that if
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3. Consider the initial value problem
9y" +12y' + 4y = 0, y(0) = a>0: y′(0) = −1.
Solve the problem and find the value of a such that the solution of the initial value problem is always
positive.
5. Euler's equation.
Determine the values of a for which all solutions of the equation
5
x²y" + axy' + y = 0
that have the form (A + B log x) x* or Ax¹¹ + Bä” tend to zero as a approaches 0.
4. Problem on variable change.
The purpose of this problem is to perform an appropriate change of variables in order to reduce
the problem to a second-order equation with constant coefficients.
ty" + (t² − 1)y'′ + t³y = 0, 0
Chapter A.2 Solutions
University Calculus: Early Transcendentals, Books a la Carte Edition (3rd Edition)
Ch. A.2 - Assuming that the triangle inequality holds for...Ch. A.2 - Show that if r ≠ 1, then
for every positive...Ch. A.2 - Use the Product Rule, and the fact that to show...Ch. A.2 - Suppose that a function f(x) has the property that...Ch. A.2 - Show that
for all positive integers n.
Ch. A.2 - Show that n! > n3 if n is large enough.
Ch. A.2 - Show that 2n > n2 if n is large enough.
Ch. A.2 - Show that 2n ≥ 1/8 for n ≥ –3.
Ch. A.2 - Sums of squares Show that the sum of the squares...Ch. A.2 - Sums of cubes Show that the sum of the cubes of...
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