(a) Prove that if f e C (R²) then a (af af %3D

Q: If g is said to be the antiderivative of the function f then O a. Inconclusive O b. O c. O d. g'(x)…

A: Here we have to choose the correct option.

Q: x+y If Z = x.n. f (***), then show that: X. Zx + y.Zy = z

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Q: f(x) = ao + a,x + azx² + azx³ € R[x] polinomu için –2 e R, f(x) polinomunun bir kökü ise x+2 e R[x]…

A: As ℝ is a ring of real numbers. So ℝ[x] is the polynomial ring that contains all polynomials in x…

Q: Prove that if F(s) = L{f(t)} then L{t" f(t)} = (-1)" d"(F(3)) ds

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Q: If f(æ) = [ V1+t° dt, then f'(x) = 1

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Q: - (7)f | dt, then f (z) 1.

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Q: Find the value of f'(7.60) from the following table using Gauss's formula 7.47 7.48 7.49 7.50 7.51…

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Q: The orthogonal trajectories of r = a0 is_ r= - +c In r = -02 + c In r + c 2 02 Inr = + c 2 ||

A: Explanation of the solution is given below....

Q: If F(s) = ℒ{f(t)} exists for s > a ≥ 0, and if c is a constant, then (7)…

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Q: 4. Define f: [0, 1] → R by if x E Qn [0, 1] if x ¢ Qn [0, 1] f(x) = (a) Prove that S° f = 0; s*f =…

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Q: t) := inf{a > 0 : wf(a) <E R² → R, we have If(x)ldr f* (t) dt

A: The measurable as,

Q: If L(x)=mx+b is the linearization of f(x) 2x-x +3 at x-1, then m3 Using L to approximate 2(1.01)…

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Q: Q1: If Z = f(x·y) + g. Prove that x² - Zxx + x· Zx = y² · Zyy + y Zy. %3D

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Q: If f(x) = x(e*+=') , then f'(x) = %3D %3D (A) (e² + æ³) æ(e*+z*-1) (B) (e" + 5æª) In(x) æ(e*+a*) (C)…

A: We have to find derivative of f(x).

Q: If f (x, y) = Vr³ + y³ In(x² + y²)e*in (zy+y') + x³y+ 10 , then f. (1,0) =

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Given a p.m.f. of x as below: (e-33x f(x) x = 0, 1, 2, ... = x! 0 O. W and y = 2x, then the p.m.f.…

A: In question, We have given the pmf of random variable X and Y = 2X then we'll find the pmf of Y. The…

Q: You know that: g(t) dt = 21 3 9(4) : %3D V3 g(9) = 3. V3 g'(x) Evaluate: da 9 + (g(x))²

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Q: Using Part I of the Fundamental Theorem of Calculus, evaluate: d d.x 10 t³ dt =

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Q: 41. Determine g(x) and all values of c such that | 8(t) dt = x² + x – 6

A: Recall the fundamental theorem of calculus:

Q: If f(x) = , dt, then f'(x) = %3D %3D t4 +1 1 Select one: a. e-4z + 1 -e b. x4 + 1 -e С. e-4z +1 e d.…

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Q: In(e) = 1): %3D d le") = = et da Use this fact to answer the following questions. To enter e" in…

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Q: k If u = f(x), then f dx x4+2x²+1 +C for some constant k . Compute kf(1). x2+1

A: topic - functions and indefinite integral

Q: = 1 – 3, h(x) = VT, then If f(x) = x* + 6, g(x) fogo h(z)-

A: Find your answer below

Q: a) If F(x) = | 1 dt, then F'(x) = t 14 1 b) If F(2) = dt, hen F'(2) = 1 c) If F(x) = / dt, then…

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Q: The antiderivative of the function f(x)= 8+ 11z is %3D O -5 + 2.8r +c O -5 + 2.8x + c 11 +1.2x + c O…

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Q: If f(x) = t°dt then = (x),f

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Q: Calculate the following assuming that E[X] = −2.3 and V ar(X) = 12.1. (a) E[5X − 2] (b) Var(−3X +…

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Q: h2 |w(x) = Let h = x1 – xo, and w(x) = (x – x1)(x – xo). Proof that max %D 4

A: Let w(x)=x-x1x-x0 where h=x1-x0Prove that wx=h24.

Q: If two functions F & G are both antiderivatives of the function f , the F (x) =G(x). (A) True B…

A: We need to explain that given statement is true or false.

Q: 4) Knowing that f = f(t), using the expressions of L[f'] and L[f"], derive an expression for d'f…

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Q: If f(x) = x(e*+) , then f'(x) = %3D (A) (e + x³) x(e²+x²-1) (B) (e" + 5x*) In(x) æ(c*+z*) (C) (e* +…

A: To find f'(x) for the given function

Q: Suppose E(X) = 4 and E[X(X – 1)] = 25.5. (a) What is E(x2)? [Hint: First verify that E[X(X – 1)] =…

A: Given: EX=4EXX-1=25.5 So, a) EX2-X=25.5EX2-EX=25.5EX2=25.5+4=29.5

Q: If f(x) = xe"+æ") , then f'(x) = %3D (A) (e² + x³) x(e*+a°-1) (B) (e* + 5x4) In(x) xe"+x*) (C) (e* +…

A: See the details solution in below

Q: Suppose f(1) = 0,f(3) = 1,f'(1) = 2 , and f'(3) = -3. Evaluate Sxf"(x) dx. %3D

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Q: Calculate E(X³), where X has the following PMF: .5 x=1 f(x)=.3 x=2 2 x=3

A: Given that  PMF of X is  x 1 2 3 f( x ) 0.5 0.3 0.2

Q: Determine E (X) and V (X) y f(x, y) -1.0 -2 1/3 -0.5 -1 1/6 0.5 1 1/6 1.0 2 1/3

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Q: 4. Decompose into f(x) and g(x) such that h(x) = f(g(x)). %3D (a) h(x) = (3x + 2)² f(x) =_ g(x) =,…

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Q: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: A function is given by, gx=ddx∫-2xet-ln2t+1dt. The objective is to find the second derivative g''x…

Q: S f(x) = x² – 2x + 6 x > 1 x4 + 2.x3 + 2 x <1 Show that there c E (-2,3) such that f(c) = 4. (Don't…

A: topic - continuity and limits

Q: If f (x) = | e'f(t) + e* dx then f(x) is equal to 2ee® –1 +1 + 1 2ee-1 2ee" –1 – 1 ee -1 + 1

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Q: • In z Find F" (2) if F(x) et dt a² _4 O A. 1 O B. 0 Ос. -2 O D. -4 O E. –3

A: Given:         Fx=∫x2-4ln xet dt                 =etx2-4ln x                 =eln x-ex2-4…

Q: Consider the function f(x) = 8x - 8x2 + 4x – 3. An antiderivative of f(x) is F(x) = Ax* + Bx + Cx² +…

A: We have to find antiderivative of f(x) or integral of f(x).

Q: 6) Show that TE[f (t - a)] = e-i2mva TF[f(t)] where a e R".

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose you know that: • f(0) = - 18 f(1) = -17 • ( f (y) et dy = 10 Evaluate: [ = f'(t) et dt

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Q: If F(t) is an antiderivative of e , then F' (t) is equal to e + C 2te О- 2te + C None of the above

A: Derivative and anti derivative are opposite functions. If a function is said to be an anti…

Q: Show that TF [f (t - a)] = e − j2πνa.TF [f (t)] where aÎR *.

A: The Fourier transform of the function is represented as , it is defined as , where . Since the…

Q: if u(x) = x^2+1 and f(u) = u^2, then  df/dx = (2u)(2x) = 2((x^2)+1)(2x) you can check the…

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Q: Assuming that f(x) dx = 3, f(x) dx = 4, and f(x) dx = 8, calculate Fx) dx. %3D %3D Jo f(x) dx =

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Q: b) Let X₁, X₂, Xn-f(x) = {0x-(0*) x>1 e. w. find Suff. Comp. St.

A: Given that

Q: 3. If f(x) = -x, g(x) = 2x + 1 and h(x) = x2, find fogoh 1 point %3D %3D О А. х2 - 1 О в. 2х2 - 1 О…

A: We use fogoh=f(g(h(x))).