1) All continuous f:[0, e function oro impanding a2 x³f (x*) dx = Sxf(xldx a) show +that 6)*>o impendng *>o impending All con tnuouyf func tien f (t)dt = x,oretonx i=(りさ

Q: 1. Show that the function, defined for x E R by f(x) = 1 is uniformly continuous 1+x² on R.

A:

Q: 33. Let x² - 4y2 if x + 2y f(x, y) = 2y %3D | 8(x), if x = 2y %3D If fis continuous in the whole…

A:

Q: 7. Let S = [0, 1] × [0, 1] and ƒ: S → R be defined by f(x, y) (2x³+y², 10, Show that f is integrable…

A: Follow the steps.

Q: Show

A:

Q: 2. Show that f(r) = sin r is uniformly continuous on (0, 00). %3D

A: 2. We need to prove that sinx is uniformly continuous on 0,∞. Definition of uniformly continuous…

Q: For a continuous function f(x) on the set 2 [- 5,2], the net area Tx)dx must be -5 always positive…

A: The given question has been solved in detail

Q: ɔ that h is a continuous functi (x2 — 2, х < 6 h(x) 3= 7х + a, х 6

A:

Q: 5. If f is continuously differentiable on (0, 1] and f(1) = f (0) = -1/6, prove that dr 22 2 Hint:…

A: Continuously Differentiable Function: A function f is continuously differentiable on [0, 1] if its…

Q: (6) Are all continuous functions on ID differentiable on D?

A: we have to identify the given statement is true or not

Q: c. Show that f(x) is NOT uniformly continuous on [0, +∞).

A:

Q: Determine whether or not fis continuous at x = 1. Justify your answer and state your conclusion. 2+…

A:

Q: a) Show that the function defined as follows 1 <x<. when 2 1 f(x)= 2" where n = 0,1, 2,3,.. on 2"…

A: Given , fx=12n  , when 12n+1&lt;x&lt;12n   where n=0,1,2,3...  onf0=0  is interable in 0,1 has…

Q: Let a, b, c, d be numbers and f(x,y) be any function. Then . f(x, y) dxdy This statement is --- --…

A:

Q: Suppose that X1,..., Xn are i.i.d. following pdf given by f(x; 0) = že-5, where both x and O are in…

A:

Q: Use the results of Exercises 15 and 16 to find the area of the region Ω shown in Exercise 13.

A: In questions 15 and 16, we can find the area of the bounded region by using the definite integral…

Q: กำหนดให้ f(x, y) = xy cos.x x² +3y²

A:

Q: Show that the function f defined on [0, 1]'by the conditions 1 f(x)=2rx when 7=1, 2, 3,...... És…

A:

Q: 4. ·| cotl t• dt 0. lim limitinin değeri kaçtır? n In(x + 1) a) 3 b) 1 c) O 2 d) 4 Boş bırak

A:

Q: 4. Let f: [a, b] → R be integrable. Define F: [a, b] → R by F(x):= == f(t) dt Show that F is of…

A:

Q: (3) Determine the values of a for which x4 + y* , if(x, y) # (0, 0), (x² + y?)ª f(x, y) = ,if(x, y)…

A: solution.

Q: 10. If f(x) and F(x) then f(2x)dx = are continuous functions such that F'(x) = f(x) on R, %3D %3D

A: We have to solve given problem:

Q: 7. Prove that if the functions f and o are bounded and integrable in [a, b], then 6. 9. f(x) $(x) dx…

A:

Q: Let f(x, y) = Scosy.sinx, x # 0 cosy, x = 0 Is f continuous at (0,0)? Is ƒ continuous everywhere?

A: We have to check whether the given function is continuous at x = 0 or not. Also, check whether it is…

Q: 2. If f is continuous on [0, 1] such that x* f(x) dx=0, for n=0, 1, 2, 3,.. then show that f(x)3D0…

A:

Q: Let fc Cx)= Vx if osxs 4 c.(x-4)+2 if x>4 denotes a real constant. - where C Show that lim fe (x) =…

A: The function fcx=x,              if 0≤x≤4cx-4+2   if x&gt;4. Where c is a real constant. We have to…

Q: 크) Prove that va +b 0. Prove that f is uniformly continuous on [0, 0).

A:

Q: Is the set {sin nx , cos mx} an orthogonal set with respect to the inner product on the set of all…

A:

Q: 2. Show that the function f(x) = cos x is uniformly continuous on

A:

Q: If fis integrable on [a, b], then a. f(x) dx = S-rx) dx c. - f(x) dx = S"f(x) dx b. F(x) dx = - ,…

A:

Q: Suppose that a continuous function g satisfies: | = 36 and g(x)dx | 9(2x)dr = 15. 0. : = =p(= |…

A:

Q: Let (s n(x-y) |x|+ly\ = 0 f(x, y)={ |x|+|y]| (0, (x, y) = (0,0) Is f continuous at the origin? Why?

A: The continuity of the function can be checked by checking the limits of the function at the point.…

Q: 4.6 Lemma Let a be a curve in R' and let f be a differentiable function on R'. Then d(f(@)) a'(S] =…

A: We will apply the extended Chain Rule of differentiation to prove the given Lemma.

Q: Suppose that X is a continuous unknown with -2 < S2 with PDF denoted f satisfying $ (2) = c (4 –…

A: i) we know that the total probability should be one means the area under the PDF should be one.…

Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y,z) = In (5z° - x-y² - 3) 1 b.…

A: In this problem, we have to check condition for having the function continuous.

Q: 3. Prove by using the Squeeze Theorem, or otherwise: 1 t2 dt is continuous at 0. T sin t (a) (b) 1+…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: I. Show that the function f defined by 1, (x, y) = (1, –1) f(x, y) = { x2 + y (x, y) # (1, –1) x + y…

A:

Q: 1. If g(x) is a continuous function on [2 ,9] such that , g(x)dx = 25 and ,9(x)dx = Find value of…

A: Using the properties of definite integral, it can be written as follows.

Q: (5) Prove that if f is continuously differentiable on [a, b], then |f(a) – f(b)| a – b max f'(x)|…

A:

Q: Consider a function ƒ : [0, 1] → R defined by f(x) = x(x³ - 1). (a) Can we apply Rolle's Theorem to…

A:

Q: alue of c that makes the following function continuous: S 1+ cx if x 2.

A:

Q: ® let f:X→R Cunt f X is bounded $ clused then f is uniformly conto

A: We have to prove that f is uniformly continuous if f is continuous, bounded and closed.

Q: f(x, y) = ´x cos(y) + y(e² − 1) xy 0 x=0 x = 0.

A: Given function is fx,y=xcosy+yex-1xy,     x≠00,                                     x=0. To prove:…

Q: All continuous functions are integrable. A True B False

A:

Q: 2. Let f (x) = cos-. Show that f is NOT uniformly continuous on (0,1).

A:

Q: Assume that J is continuous on [0, 3 and differentiable on (0, 3) with f (z) > 6 for each z in (0,…

A:

Q: true or false with reason c) If f and g are continuous and f(x) ≥ g(x) for a ≤ x ≤ b, then…

A: Given: If f and g are continuous and, then  integration ∫abf(x)dx&gt;∫bag(x)dx

Q: Please just do 3(b).

A: (b) To prove that the given function is not Riemann integrable using Lebesgue;s theorem

Q: Determine where h(x) = sin(x- Sx + 2) is continuous. %3D h is continuous on the interval [0, co). h…

A:

Q: (5) Suppose that fis continuous on [a, b]- f(x) ≥ 0 Vx = [a,b] and [f(x)dx = 0. Prove that f(x) = 0…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.