1. а)Suppose that f'is defined recursively by:f(0) = 5 and f(n+1) = 2 fn+5. Find f(1), A2), A3) and f(4)?b)For which positive integer n is it true that 2" >n³?c)Prove your answer in (b) above using mathematical induction.d)Give a recursive definition of the sequence {an}, n= 1, 2, 3...ifan = 2" + 1е)Use your definition in (d) above to find a10, and a15f)Let A = {1, 2, {{1,2}}}. Find the power set P(A)2. а)Define the following with an example:i)Contradictionii)Propositionb)Show that (p → q)^ (p→r)is a Contingency.с)Use quantifiers to express the statement “if somebody isfemale and is a parent, then this person is someone's motherd)Let p and q be the propositions:p: I will do every exercise in this bookq: I will get an 'A’ in this courseWrite the following propositions using p and q and logicalconnectives.i)For me to get an 'A’ in this course it is necessary andsufficient that I do every exercise in this book.ii)Construct the truth table for your propositin d(i) above.e)i)Write down the output Boolean expression using p, q and rfor the circuit gates below:ii)if p = 1, q = 0 and r= 1 find the output signal for thecircuit below:r

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Answered: 1. a) Suppose that fis defined…

1. a) Suppose that fis defined recursively by: f(0) =5 and f(n+1) =2 fn+5. Find A(1), A2), A3) and f(4)? b) For which positive integer n is it true that 2" >n³?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

1. а)
Suppose that f'is defined recursively by:
f(0) = 5 and f(n+1) = 2 fn+5. Find f(1), A2), A3) and f(4)?
b)
For which positive integer n is it true that 2" >n³?
c)
Prove your answer in (b) above using mathematical induction.
d)
Give a recursive definition of the sequence {an}, n= 1, 2, 3...
if
an = 2" + 1
е)
Use your definition in (d) above to find a10, and a15
f)
Let A = {1, 2, {{1,2}}}. Find the power set P(A)
2. а)
Define the following with an example:
i)
Contradiction
ii)
Proposition
b)
Show that (p → q)^ (p→r)is a Contingency.
с)
Use quantifiers to express the statement “if somebody is
female and is a parent, then this person is someone's mother
d)
Let p and q be the propositions:
p: I will do every exercise in this book
q: I will get an 'A’ in this course
Write the following propositions using p and q and logical
connectives.
i)
For me to get an 'A’ in this course it is necessary and
sufficient that I do every exercise in this book.
ii)
Construct the truth table for your proposit
in d(i) above.
e)
i)
Write down the output Boolean expression using p, q and r
for the circuit gates below:
ii)
if p = 1, q = 0 and r= 1 find the output signal for the
circuit below:
r

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