2. Let H=10 so f (r,b)=[?][?]1+1006 100r Compute O[?][?]f 3. Let r=100 and b=2 so 9(H)=[?][?]100H² 1+2H? -2 Compute Jim g(H) Be sure to show appropriate work and justification in your answer.

Q: [1] The forward-difference formula can be expressed as h h2 f'(xo) = [f (xo+ h) – f(xo)] f"(xo) f"…

A: Consider the provided question, The forward difference formula is given as,

Q: Q3 Prove that In Coth x 1

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Q: 3) Prove that ae*+be-x a) b b > 0 ex+e~x

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Q: 19. Let f(x) = e*. Then, for all n, %3D f(n) (x) = e* and f(n)(0) = 1 It follows that T„(x) = 1+…

A: We have given;

Q: Evaluate h(2), where h = (gon. s (2) = –ig(2) =?+1 1 f (z) . h(2)

A:

Q: Let f(2)= ¹5 and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of…

A:

Q: TQ residue of f(z) = e (z – 1) (z + 9) at z = -9 is 10e-9 :Select one True False

A:

Q: 2.2 If fe R(a) on [a, b] and if Saf da prove that a must be constant on [a, b]. = 0 for every f…

A:

Q: For all n ≥ 1, let an = (a) Find a1, a2, A3, A4. (b) Computea. i=1 (c) Computea. i=1 (n + 1)² n!…

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Q: 3.18 Suppose if x = 0, f(x) = if z e (. where n e N. Prove: f € R[0, 1], even though f has…

A:

Q: Q53- X--) (xij-Xi - X.j+X)=Zero 13D 「に )に prove that e to

A: We need to prove the given equation.

Q: 3. Prove the Archimedean Property, if x ER. then there exists K E N such that r SK.

A:

Q: 1. What is the value of the 4th iterate of f(x) = 31 if xo =-2? Round to three decimal places. %3D…

A:

Q: (a) Find the least positive k E N such that 3* =10 1. (b) Using this k, prove: for all m e N, 3m =10…

A: (a) find the least positive k∈ℕ such that 3k≡10 1 b) using this k prove that : for all m∈ℕ 3m≡103m÷k…

Q: 10. Show that (ii) If f(t) t2 if 0 1, then L 2(1-e-) S

A: Step:-1 gt = g0t,   0<t≤t1g1t,   t>t1 then gt =g0t +u t-t1  g1t - g0t  And  L  u t-t1  gt…

Q: (a) Let a > 0. Using the substitution t = In x or otherwise, prove that In a e 4/a² - e 2t dt =a5…

A:

Q: Compute 5f – 7g, given that f(r) - and g(z) - e. -1) "(z-1) Se

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Q: 23. If u = f(x), then +2x² + 1 k + C for some constant k . x² + 1 Compute kf (1). (a) ¼ (b) – ½ (c)…

A:

Q: We decide that 2 such that f (2) = 8 will be one of our initial points. Which of the following are…

A: Given that,

Q: Let f(2)=³ and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of Ac…

A: Given that             fz=z4-5z2      and    C=z∈ℂ : z=1.

Q: If f:(0,∞)→Rf:(0,∞)→R is defined by f(x)=xln(2x)f(x)=xln⁡(2x) for every x∈(0,∞),x∈(0,∞),  then…

A:

Q: HW klx) = 2x+5 ㄱ 1. Find ke-¹(x) 2. Prove by kokorklok

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Q: Let h(x) = e" + 2x. Use the Intermediate Value Theorem to show that e" + 2x = 0 has at least one…

A: First it is required to show that h(x)=0 has at least one solution, where hx=ex+2x

Q: 4 The approximation of the root x of the function f(x) - In(x+3)-x+3 accurate to within 10 using…

A: Sol:- Here ln(x+3)-x+3=0Let f(x)=ln(x+3)-x+3a=4,b=5,f(a)=0.9459,f(b)=0.07941st iteration :x0=4 and…

Q: 84. a. Prove that e > 1 + x if x > 0. b. Use the result in part (a) to show that e 21+x + r.

A: Answer (a): To prove : ex≥1+x if x≥0 The given inequality can also be written as: ex≥1+xex-1-x≥0

Q: (b) Prove or disprove: f: 41o → Z20, [r|10 + + r2|20 is well defined.

A:

Q: Show that g(t) = t2tant takes on the value ½ for some t in [ 0 , π/4 ].

A: gt=t2tant on the interval 0, π4. When t=0, g0=02tan0=0 When t=π4, gπ4=π42tanπ4=π2161=π216=0.6168

Q: For f(x) = x³ - x +4, compute the formula for n+1 in Newton's method. - In +4 - 3h - In 3a급-1 | In +…

A:

Q: Let s: = ∑_(k-1)^(n=0)rk. Compute s(1-r) = s - rs, and solve for s. Then prove r ≠ 1, for…

A: We need to prove that the sum S= (1-rn)/(1-r) when r is not equals to 1.

Q: Suppose x-j, for j-0, 1, 2, 3 and it is known that Find Po123(1.5). P₁1(x)=x+1, P₁2(x)=3x-1, and…

A:

Q: 6. so be it r = 3xi + yi – 2zk and f (r) : -- where |r| = r find all of grad(f) and div (-)

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Q: Prove for r ≠ 1 that ∑_(k=0)^(n-1)(rk)=(1-rn)/(1-r). If ∑_(k=0)^(n-1)(rk), then compute s(1−r) =…

A:

Q: Calculate dIn |2 – 1|/d In a as a function of 2 and w; by differentiating 2(a) – 1 = H²a? to show d…

A:

Q: Differentiate f(N) = (N) = 0 bN² + N with respect to N. Assume that b and K are positive constants.…

A:

Q: (c) Use part (b) to show that Fn-1 00 00 (-1)"+1 - Fn Fn+1 n=1 Fn+1 n=1

A: Consider the given information: The part (b) states that  -1n+1=Fn2-Fn+1Fn-1 To show that,…

Q: (c) Derive the following formulae (i) Σ Fra"(n+1) 2 (ii) n(n + 1) (2n + 1) 6. r=1 (ii) 2 n(n+1 2 r-1

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Q: -4s? – 5s + 14 2s +1 + s2 + 72 5 3 + 86 1 4s -] Let G(s) = - - 5)³ (s – 2)(s – 4)(s+1) s2 + 6s + 34…

A:

Q: 10. Show that S t2 if 0 1, 2(1 - e-) then Ldf %3D

A: Laplace of differential equation.

Q: 50. Suppose that in approximating a zero of f by the Newton- Raphson method we find that f(c,) =0…

A:

Q: 1. a) In G = (Z43, e), find [G:H] for H = (32). b) In G = (Z54, O), find [G: H] for H = (24).

A: 1. a) Consider the group G=ℤ48, ⊕. We know that the set ℤn=0, 1, 2, …, n-1 forms a group under…

Q: Let f (x) = -2r, de fined on -1, 1], then L (P ) = 2 (n– 1) 2- 4 (n+1) 4 (n – 1) 4 (п-1) 2n2

A: We need to find the lower Riemann sum

Q: Prove that the value of the expression (а — 1)(а — 3)(а — 4)(а — 6) + 10 is positive for every a E…

A: The critical points for the function are the set of values where the function attains its maximum…

Q: x+1 Q1/ Prove that coth-1 x = 2 x-1

A: In this question we need to show coth-1x=12lnx+1x-1.

Q: (a) Compute /(2) dr, given that f(b) 3 and that | af'(a) dr b(1 + f(-b)). (b) Computei (2) dz. given…

A:

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: 1. Evaluate the following. Use only the rules and techniques of integration presented in the module.…

A: To evaluate the given integral.

Q: 9. Suppose that N(h) is an approximation to M for every h > 0 and that M = N (h) + K,h+ K,h? + K3h…

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Q: 4.1.c Find the efficiency of ô, relative to 02. eff(@,, Ô2) = ? 4.1.d Prove that ô, and ô, are…

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Q: Let f(n) = 2n – n? + 10n – 7. Show that f(n) is O(n³) using specific values of C and ng-

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Q: Suppose that in the forward difference formula of order O(h) for f'(xo), h = 0.2 and |f"(c)| < 0.5,…

A: hf''(x)/2 ≤0.2×0.5/2 ≤0.05