Thinking Mathematically (6th Edition)
6th Edition
ISBN: 9780321867322
Author: Robert F. Blitzer
Publisher: PEARSON
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Chapter 11.2, Problem 44E
Use an appropriate permutations formula to solve Exercises 41-56.
Suppose you are asked to list, in order of preference, the three best movies you have seen this year. If you saw 20 movies during the year, in how many ways can the three best be chosen and ranked?
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Find g[f(-7)].
f(x) = x² + 1; g(x)=-5x-1
Find the x-values where the following do not have derivatives.
8.
For each of the following functions, determine whether or not it is (i) injective
and/or (ii) surjective. Justify why or why not.
(a) fiZZ defined by fi(n) = 2n.
(b) f2 RR defined by f2(x) = x² − 4x+7.
:
(c) f3 Z {0, 1} defined by f3(n) = 0 if n is even and f3(n) = 1 if n is odd.
(d) f4 Z N defined by f4(n) = 2n if n > 0 and f4(n) = -2n-1 if n < 0.
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- 2. Disprove the following by finding counterexamples: 3. (a) For all sets A and B, AU (BNA) = B. (b) For all sets A, B, and C, ANBCC if and only if ACC and B C C. Suppose A and B are subsets of a universal set U. Using the set identities¹ prove the following: (a) (ANB) U(ANB) = B (b) A (BA) = Aarrow_forwardNo chatgpt pls will upvotearrow_forwardx+10+2 = 6 x =?arrow_forward
- 4. Prove: If x {0, 1} then x² - -x=0. 5. 6. Prove by contrapositive: Suppose x is a real number. If x>0 then x + 16 0. Prove by contradiction: Suppose n is an integer. Then n² - n+10. Hint: You might try organizing the proof by cases on whether n is even or odd. Is n² - n+1 even or odd?arrow_forwardLet f(x)=7x²-2x and g(x) = 5x+3. Find f[g(k)].arrow_forwardUse the method of reduction of order to find a second solution to ty"-(4t+4)+(4t+8)y = 0, t> 0 Given y₁(t) = e²t Y2(t) = Give your answer in simplest form (ie no coefficients)arrow_forward
- 1. Suppose the domain of discourse is kinds of minerals. Let A be kinds of minerals that dissolve in acid, let S be minerals that can be scratched by an iron nail, and let C be minerals that are clear. Write expressions using set operations that represent the following sets of minerals: (a) Minerals that dissolve in acid and can be scratched by an iron nail. (b) Minerals that dissolve in acid and are not clear. (c) Minerals that are either clear or both dissolve in acid but cannot be scratched by an iron nail. (d) Minerals that are neither dissolvable in acid nor scratable by an iron nail. (e) Minerals that are either both dissolvable in acid and scratchable by an iron nail or both dissolvable in acid and not clear.arrow_forwardExpress the integrand as a sum of partial fractions and evaluate the integral. 2 32s+ 32 (s²+1) (s-1)3 ds Express the integrand as a sum of partial fractions. (Simplify your answer.)arrow_forwardSolve the problemarrow_forward
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