How would you find g (A) if a) g (x) = 1. b) g (x) = (x + 1)2 . c) g (x) =⌊ (2x + 4)/3⌋ Where A = {-2, -1, 0, 1, 2}. Determine the image of every element? How would you find out f−1({0, 1,2,3}) where f(x) = ⌊x⌋. How would you justify that sequence Zn is a solution of the recurrence relation zn = -3zn-1+ 4zn-2 if zn =2(-4)n + 3 How would you find out the sequence (first five terms) using the recurrence relations and initial conditions. a) an = −2an−1, a0 = −1 How would you express each of these quantifications in English? a) ∀xP (x) b) ∃xP(x) c) ∃x ¬P (x) d) ∀x ¬P (x) The statements are “x have attended the end of the seminar” where the domain for x consists of all participants. How would you express each of these statements by using quantifiers with one or two variables as required? a) Someone in my friend circle has visited Turkey b) No one in your home owns both a motorcycle and a car. c) There is a person in your office who is not sad.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
How would you find g (A) if
a) g (x) = 1.
b) g (x) = (x + 1)2
.
c) g (x) =⌊ (2x + 4)/3⌋
Where A = {-2, -1, 0, 1, 2}.
Determine the image of every element?
How would you find out f−1({0, 1,2,3}) where f(x) = ⌊x⌋.
How would you justify that sequence Zn is a solution of the recurrence relation
zn = -3zn-1+ 4zn-2
if zn =2(-4)n + 3
How would you find out the sequence (first five terms) using the recurrence relations and initial
conditions.
a) an = −2an−1, a0 = −1
How would you express each of these quantifications in English?
a) ∀xP (x)
b) ∃xP(x)
c) ∃x ¬P (x)
d) ∀x ¬P (x)
The statements are “x have attended the end of the seminar” where the domain for x consists of
all participants.
How would you express each of these statements by using quantifiers with one or two variables as
required?
a) Someone in my friend circle has visited Turkey
b) No one in your home owns both a motorcycle and a car.
c) There is a person in your office who is not sad.
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