Find the exact error in approximating ln(sec(−0.4))by its fourth degree Taylor polynomial at ?=0.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: A linear differential operator g D is called    annihilates the functions fx if and only if…

Q: 2. Find the MacLaurin polynomial of degree 7 for the function F(x) So sin (6t²) dt.

A: SOLUTION-

Q: Explain, in terms of linear approximations, why the  approximation is reasonable. ln 1.05 = 0.05…

A: Given: (1.01)6=1.06

Q: If the population of penguins on the island in year 0 was 10,000, what is the population of penguins…

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Q: Estimate the root very near x = 0.2 of 2(x*)* - 3(x*} + 1 = 0 using the Newton- Raphson Method with…

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Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = cos x cos y at the origin.…

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Q: 5/ Use the Newton - Raphson method to estimate the root of f(x) = e - x, employing an initial guess…

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Q: Find one real root of ln(x^4) = 0.70 using five iterations of bisection method on the interval…

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Q: 3. Solve this third-order ODE by using the method of undetermined co- efficients: y" – y = exp x . -…

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Q: Find the general solution using reduction of order. 1. y''=ln(x)

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Q: Find where ln((1+z)/(1-z)) is not analytic.

A: To find: The region where the function ln(1+z)(1-z)), where z∈ℂ is not Analytic.

Q: Determine the positive real root of ln(x^2)=0.7 using three iterations of bisection and…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: Jse differentials to approximate 47. (Express as a rational number.)

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Q: Find y double prime using implicit differentiation5x^3+4y^3=1

A: We have given,

Q: In the integration of (cos y)^2 dy/(1 - sin y), what is the first step to solve the integral? Select…

A: Given integral.

Q: Find the approximate value of cos59 with the help of differential. w

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²-) < 0, ƒ (x) has a root in [0]. If we…

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Q: Establish the following integration formulas with the aid of residues: cos x - dx xt + 20x² + 64 `

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Q: Find a root of an equation f(x) = cos(x) - − using Newton Raphson method

A: Let us start solving the problem step by step  Given  Cos(x)-(x/6)=0 Let f(x)= cos(x)-(x/6) We will…

Q: Find the roots at x = 3 of function f(x) = tanh (x² – 9) with an initial guess xo = 3.2 in three…

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Q: Find Lf 0- £{[ e-axdx } by transforming e atu(t) then applying the integratiori property

A: Given :I=∫0te-axdx Laplace Transform u(t)→ℒu(t)us=∫0∞e-stu(t)dt we need to find: ℒ∫0te-axdx

Q: What is the approximation of the value sin (1) obtained by using the fifth-degree Taylor polynomial…

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Q: A 1125 m³ open-top rectangular tank with a square base x m on a side and y m deep is to be built…

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.34). L(x) =…

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Q: Let F(x) = / sin(8r²) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.6 Use this…

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Q: Investigate the root of the equation x+Ln x-5 = 0 in the range [3.2,4] using the Regula-Falsi…

A: Consider the given equation whose root is required to calculate.

Q: (b) Use the total differential dz to approximate Az. dz = X

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Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

Q: y" +Zy+3y=sin (3x)

A: Given that,  y''+2y'+3y=sin(3x) The auxiliary equation is m2+2m+3=0m=-2±4-122=-2±2i22=-1±i2…

Q: 2. Compute for a real root of 2 cos a – sin Va = + accurate to 4 significant figures using…

A: In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.…

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () < 0, f(x) has a root in [0]. If we use…

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Q: . Approximate the value of V65 by Newton-Raphson method letting xo = 5.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the Fourier integral of the function f(x)= e* when x> 0 and f(-x) = f(x) for k > 0 cosix and…

A: Fourier integral, for even function

Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of…

A: Consider the given: The Maclaurin series for sin x centered at x = 0 is:…

Q: 2. Use the identity of inverse hyperbolic function to solve cosh-(2 – a2) = ln 2, for |æ| < 1.

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: See the detailed solution below.

Q: 6. S(x)= In(tanh 5"

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Q: Use differentials to approximate radical (48.7)

A: Ne need to approximate √48.7 using differentials.

Q: Eliminate the arbitrary constants x = -ln t , y = at + bt^2

A: given  x=-ln t , y=at+bt2 claim- to eliminate the arbitrary constants

Q: 3. Use Log Rule to integrate. J6x-5 dx a. 6х-5 b. S- 1 dx x Inx

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Q: Find y double prime by implicit differentiation8x^2+y^2=4

A: We have given

Q: 18. Show that Vxª + x and Vx* x→o by showing that they both grow at the same rate as x² as x' grow…

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Q: Find the total differential of z = In (2x – 3y).

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Q: Show that the following functions all grow at the same rate using properties as x co: fi(x) = x°,…

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Q: Calculate for one real root of tan x = 4x with xo = 1.2 up to four decimal places using the…

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

Q: Use a linear approximation of f(x)=cos(x) at x=5π/4 to approximate cos(222∘)

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Q: Use the Romberg integration to evaluate. 3 xe*dr With an exactitude e =0.5%

A: Given ∫03xexdx whose step error should be εs=0.5%. We use the Trapezoidal rule…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: arc sin z = -i log(iz + V1- 22).

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The given function = 10x+ 9x2-sin6x