3.5 Suppose f E R[a, b] and g(x) = f(x) except at finitely many points in [a,b]. Prove: g E R[a, b] and Lote) da = f(a) dz. f(x) dx. (Hint: Write h(x) = g(r) – f(r) and apply Exercise 3.4.) For reference 3.4 1 Suppose h(1) = 0 except at finitely many points 11, 12, . .., Prove: h e R(a, b) and Ek in (a, b]. h(x) dr = 0.

Q: 26) Consider the function S1 if 0<x < 1, х ifx€ [1,2]. f (x) = Let F(x) = So f(t)dt for each a € [0,…

A:

Q: 4. If [æf (x) + 2] dæ = x³ – a² then find the function f (x). 3 A) 2 3 B) 2+ C) 3- 2 E) 2– D) 3+ --…

A: The given equation is x∫x fx+2dx=x3-x2.

Q: 3.23 Prove or give a counterexample: The function |f| € R[a, b] + ƒ € R{a, b].

A:

Q: Exercise 6. Let f(x) = 2x-5logx. Then f(x) is а. О(х) b. O(x²) с. О(Зx?) d. All of these

A:

Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

A:

Q: For which values of a ∈ R is the function f(x + iy) = (a2x - axy) + i(- ax2/2 + ay), an entire…

A:

Q: Find the exact value of F. dr using any method. b. F(x, y, z)= C is the line segment from (1, 0,…

A: The given vector field is Fx, y, z=yz, xz, xy+2z. We have to find ∫CF·dr.

Q: g(x) = V4t + 5dt. Find g'(2). Let 3-x

A: We have given that  gx = ∫3-xx24t+5dt We have to find g'2 for that we have to use Leibniz integral…

Q: 2. Let f:Z→Z be the function given by fAn) =3n+1. a. Is fone-to-one? Briefly explain why. b. Is…

A:

Q: R.4. Let f:R→R be defined by f(x)= 2x² – 3, and let A=[-5,3]. Find f[A]. f'[4]: S[S"[4] , and…

A:

Q: 7. Let h(x) = V3x – 5. Define two functions f (x) and g(x), where h(x) = g(f(x)).

A: You must have an idea about composite function to understand it better.

Q: Prove that if a(x) = |r|, the absolute value function, then a E C(R). (Use 1.9.)

A:

Q: 19 For X = {1, 2, 3} and Y= {a, b, c), functions f. X - Y and g: Y-X are defined as follows: 1. NT 2…

A:

Q: The polynomial of degree 4, P(x) has a root of multiplicity 2 at a = 2 and roots of multiplicity 1…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Consider the function f(x): = 5x³ - 7. 20 4 a. Over what interval(s) is f concave up? (If f is never…

A: fx=320x5-34x4-5x3-7

Q: 1. Let f(x)=x² - x, xeR then f(f(f(v2))) is: -34 + V2. b. 2/2 +34. c. 34+2/2. d. 34– 2/2. e. 2/2 -…

A:

Q: Which one of the following relations is not a function? O ((x.y): r, y ER and r + y² = 1) O ((x.y):…

A:

Q: 10.30

A:

Q: f(x,y) = x² + 3xy +y² fonksiyonu için fex (2,3)]. [fyy (2,3)] – Fzy (2,3)]? =

A: The answer is, (-5) The detailed solution is as follows below :

Q: (2) I Let (x, y) E R X R. Consider the following functions from R? to R? r((x, y)) = (-y, x) and…

A: We have to find the order of r and s. Here rx, y=-y, x and sx, y=x, -y where x, y∈ℝ. First, we have…

Q: Question 2: show that if T (X,., X„) is the UMVUE of g(0), then aT(X1,.. , Xm) + b is the UMVUE of…

A: Given that T(X1,X2,....,Xn) is UMVUE for g(θ).Hence, E(T(X1,X2,....,Xn)) = g(θ) and for any other…

Q: 2.5.33. Prove that the image of the function f: R → R , f (x) x2 is the interval [0 ,1) . Do not use…

A: The given function f:ℝ→ℝ f(x)=x21+x2 We have to show the image of the function is  [0,1)

Q: (14) Let f.g E L2[a, b]. Prove If +gli + |f – gli = 2|f3 + 2|g|3 -

A:

Q: Exercise 3.11. Consider the following two functions: 1. f:R → R defined by f(r) = 4x – 15. 2. g :…

A:

Q: Exercise 1.16. 1. Show that for any function f Ep(æ|9y)f(y) = f(3)

A:

Q: Let f(t) = t for t > 0, and g(t) = sin t for t > 0. Compute f * g.

A: If we are taking * as the product, then f*g=fg=t sin t for t≥0. Taking * as convolution: We know…

Q: 1. Determine whether f is a function from Z to R if а. f (n) %3D tn b. f(n) = Vn² + a %3| 1 с. f (n)…

A:

Q: Let f. R> R defined by f(x) = g: R> R defined by g(x) = Vx and h: R>R defined by %3D 3 h(x) 2x – 5…

A:

Q: Let f(r) = 2. 1 + Find f(1/2) 1. Find the domain of f ii.

A: Given data is: fx=11-21+11-x Calculate the value of f12 and the domain of the function.

Q: Let f(x) = and f(g(x)) x-2 = x+3 2(2x-3) a. Find g(x). b. Determine the domain and range of g(x).

A: Given, fx=1x+3 and fgx=x-222x-3

Q: 2. Let a = (a1,..., an) € R" and let f : R" →R be defined by f(x) = (a, x). Compute the following:…

A:

Q: Sx, if xe Q if x ER – Q. f(x) = Using only the definition of derivatives and Lemma 4.2.2, determine…

A:

Q: 3. Let f (x) = x ² + 8x + 14. Find all the values interral C-G ,2) such that f (c) = 0 of ċ in the

A:

Q: 5. Find the x-coordinates for all points of discontinuity for f(x)- 「X316, xśl x〉 1 2 c. 1, 32d.…

A: First we check the limits as x approaches to 1 from left side and right side .

Q: 3.13. Let V D(0. 1). Suppose that f e C(V) NH(V), f(0) = 0 and |f(2)| < 1 for all z e V. Show that…

A: Given V=D(0,1) which is open disk with radius less than one. which is z&lt;1 Since f∈C(V¯)∩H(V)…

Q: Inverse Functions beduined Let f: R→ R be defined by f(x) = 3x +2. Show that f is bijective and find…

A:

Q: Let f(x, y) = x for y=0 and 0 for y+0. Evaluate each of the following or if they do not exist, state…

A:

Q: 6. Let f be function such that f(-a) = - f(2) for all If a %3D х. | f(2)dz = 5, then L2) +0)dz =…

A: With the help of definite integral property we solve this.

Q: Z is the set of integers, R is the set of real mumbers. 1. Functions f, 9, and h are defined as f:R…

A: