Let ƒ be the following function on interval [0, 1] x € Q 1-1 x¢Q f (x) = (a) Let Q be the following partition of [0, 1], Q = {0, 3,1}, compute U(f, Q), L(f, Q) (b) Prove: Let P = {0 = x0, x1, X2, • • • , X'n = 1} be an arbitarty partition for [a, b], U(f, P) = 1, L(f, P) = - 1 (c) Prove that ƒ is not integrable on [0, 1].

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

A:

Q: 10 5. Consider a function f (x) that satisfies all the conditions listed. i. fis defined and…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let R={(x,y) ERxR: |x| = |v|). Then R a function on R. оо True False

A:

Q: 3. Let f be continuous on [-1, 4] and differentiable on (-1,4). If f(-1) = –1 and f(4) = 4, then the…

A:

Q: If f(x) = 1+ then the interval(s) of decreasing is(are) Select one: O (-00,-1]U[1, 0) O -1,0) U (0,…

A: f(x) = x + 1x Differentiating with respect to x: f'(x) = 1 - 1x2   .......................using…

Q: Let f: [2, 7] → [0, ∞) be continuous in [2, 7] a (2,7). Then prove that there exists at least one…

A:

Q: Given the vectors a a b -10 -6 9 U•V 4 -10 -6 9 5 S 7 y- 5 m 2 3 -2 Find a match for each of the…

A: Since you have posted a multi subparts question according to guildlines I will solve first(a,b,c)…

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: Suppose that f : A → B is a function, C C B and D C B. Prove that Š (C – D) = } (C) - } (D).

A: Solution :-

Q: 5. Prove that the function f: Z → Z defined by f(x) = 3x + 1 is one-to-one.

A:

Q: If f is a function from X to Y and C, D are subsets of Y then A O f(C-D) =f(C)-f (D) B f'(Cn…

A:

Q: Let f(x, y, z) = (2x - 7) * (y +3z). (a) Construct the computational tree for the forward-mode…

A:

Q: Exercise 4. Let F and G be homothetic functions in two variables. Is their sum homothetic? [Hint,…

A: We will use the fact that the MRS of a homothetic function is always homogeneous of degree 0. Let…

Q: A on S is a function from S×S into S.

A:

Q: Find continuous functions f1, f2, f3, f4 defined on the open unit interval I = (0, 1) (i.e.…

A: 1. f1(x) = (M1 - L1)x + L1, for all x in (0, 1)  This function is linear and maps (0, 1) onto (L1,…

Q: Determine L[f]if 0, f(1) = {1- 1, 0 2. 1,

A: Given that, A function f(t), t ≥ 0, its Laplace transform F(s) = L{f(t)} is defined as

Q: Let A, B C X be subsets and f : X → Y a function. Show that ƒ(AÑ B) ≤ f(A)Ñ ƒ(B)

A:

Q: If f(x)=14-x^(2) and g(x)=\sqrt(x+31), compute g(f(3)). Simplify your answer as much as possible.

A:

Q: 1 If the function f is continuous on [a,b], then there exists at least one number C in [a,b] such…

A: If the function f is continuous on [a, b], then there exists at least one number C in [a, b] such…

Q: What is the range of the function f(x) = = x + b -, a, b = R and a, b =0? xa

A: range of fx=x+bx-a

Q: Find f(2021) if function f satisfies following conditions: f(1)=1, f(x+y)=f(x)+f(y), for all x,y…

A:

Q: 13. Let the function f: [a, b] in R be continuous and one-to-one and such that f(a) < f(b). Let c…

A:

Q: How many functions f:R→R  exists such that : 2f(x)+2f(y)=f(x+y)+f(x−y)+2y holds for all real x and…

A: By choosing x=y=0. Also by choosing x=y we can see f(2x)=4f(x).  Moreover choose x=0 and use f(0)=0,…

Q: Let φ1(x) = 1, φ2(x) = x/|x|, φ3(x) = x^2 − 1/3 for −1 ≤x ≤1. Show that (φ1,φ2,φ3) form an…

A:

Q: for If f (2) is a regular function of z, prove that f (2) 2 = 4 | f'(2) 1?. %3D ve I f12) 1? =4 |…

A:

Q: Suppose f: R → R is a function defined by f(x) = x³. (a) Find f([-1,1]) and f-¹([0, 8]). (b) Show…

A: We shall use the intermediate value theorem to answer this question

Q: Let f1, f2, .. fn be n real-valued, differentiable functions.- Prove that e :[fif2 ... fn] = (fif2…

A: We have to prove that the given formula.

Q: The linear functional F: R^2[x] -> R is defined by the formula F: p -> ∫(from 1 to 0) p(t)dt.…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let g: RxR → RxR be a function defined by g(x, y) = (x², x-y). Suppose that X = Rx{0} and D= {(a, a)…

A: Bartleby Guideline : ''Since you have posted a question with multiple sub parts , we will provide…

Q: Let f: X --> Y be a function, and let U be a subset of X.  (1) Prove or disprove that f maps X \ U…

A:

Q: Which of the following interval is f(x) = O (2, +∞0) O [2, +∞0) 0 (-∞0, +∞0) ○ (0, +∞) 1 Vx…

A:

Q: 3. The function f(m, n) = 2"3" is a one-to-one function from N x N into N. (a) Calculate f(m, n) for…

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.