|| I(f) sup {Lp(f)| P is a partition of [a, b]} a

Q: Consider f(x) = 36 - x2 over [0,6]. Let P = {0,2,3,4,6} be a partition of [0,6]. Find U(P,f).

A:

Q: Let f: [a, b] → R be a bounded function, and let P be a partition of [a, b]. Let P be a refinement…

A:

Q: Prove that f(x) = 5x2 + 3x – 26 is θ(x2)

A: Given: f(x) = 5x2 + 3x – 26 is θ(x2)

Q: Let 2. x = 0, f(x): x/2, 0 < x <2, 2x 2, 2<x ≤ 6, - and let P be the partition of [0,6] given by P =…

A: Step 1: Step 2:

Q: 6. Let f be continuous on [a, b]. Show ffdF = f(x) [F(b) – F(a)] for some x € [a, b].

A: This is a consequence of the intermediate value theorem

Q: Let F be the set of all functions of the form f : N {0, 1}. Also, let G be the set of all functions…

A: We have to find all possible options that are correct for the given question.

Q: Let g : B → N × N where B C Z given by g(m) = (|m| + 2, |m| + 3). Choose all subsets B such that g…

A:

Q: Prove that P[X |Y ] = (P[Y | X] · P[X] ) / P[Y]

A: From the definition of conditional probability, for two events X when Y is given PX|Y=PX∩YPY

Q: Find the norm of f(x) = √√1-x² on the interval [- 1,1]. 2√3 3 O O O W|N H

A:

Q: Determine b so that f(x) is continuous if O 8 x + 6 xS 6 f( x ) = D O 2 x2 + bx +10 x > 6 b =

A:

Q: Suppose f : A → B is an injective function, and {A;};e1 is a partition of A. Prove that {F (A;)};er…

A:

Q: Let f be a continuous, increasing function on [a, b] and let P be a partition -a for all i = 1, 2,…

A:

Q: Prove that if f is a constant function on [a, b] then f = S(f,P) for any tagged partition P of [a,…

A: This is a question of R integration.

Q: O Find the largest value of A such that the function f(x) = x + 1x? - 4x + 6 is decreasing for all x…

A:

Q: Let f : R → R and ECR. Prove f is continuous iff f-¹(E) is closed whenever ECR is closed.

A:

Q: function g : Z → Z is defined as g(n) = |n| + 1. Show that this function is not injective and not…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.