Exercise 1. • Find the antiderivatives of f(r)= %3D • Compute F(x) where Fl6) = L. %3D

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Exercise 1.
• Find the antiderivatives of f(r) =
• Compute F(r) where
F(6) = [
%3D
Exercise 2. Find the general integral of
1" - (2+ a)x' + 2ax – 4 = 0
in dependence of a e R, a + 2. Are there values of a # 2 such that any solution of the differential
equation posses an horizontal asymptote as t- -oo?
Exercise 3. Given the function of two variables
f(r, y) = x"
find its domain. Then, find the equation of the tangent plane at (1, 2, ƒ(1, 2)).
Exercise 4. Consider the following matrix depending on the real parameter h:
1 -2
A = 2 -4
h 2
-2
• For h = -1 find, if possible, a basis of R made of eigenvectors of A.
• Find the eigenvalues, for every given h.
Find all the values of h for which the matrix A is diagonalizable.
Transcribed Image Text:Exercise 1. • Find the antiderivatives of f(r) = • Compute F(r) where F(6) = [ %3D Exercise 2. Find the general integral of 1" - (2+ a)x' + 2ax – 4 = 0 in dependence of a e R, a + 2. Are there values of a # 2 such that any solution of the differential equation posses an horizontal asymptote as t- -oo? Exercise 3. Given the function of two variables f(r, y) = x" find its domain. Then, find the equation of the tangent plane at (1, 2, ƒ(1, 2)). Exercise 4. Consider the following matrix depending on the real parameter h: 1 -2 A = 2 -4 h 2 -2 • For h = -1 find, if possible, a basis of R made of eigenvectors of A. • Find the eigenvalues, for every given h. Find all the values of h for which the matrix A is diagonalizable.
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