Find General Solution on this Diffential E Qution by using (uC set) =e +Sin X

Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

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: .Find the estimate for the root of f(x) = sin x + cos (x² + 1) – 1using Bisection methodx, = 1. 5,…

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Q: Use integration by parts to show that, for n > 2, 1 cos a sin"-1 n 1 sin"-2 xdx. n - sin" xdx = x +…

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Q: S find the Voutofeguatin 3x€-1rinthe interval Co,1] bg using:- - Bisectin method

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Q: What must be the measure of ZX in order for ARST to be similar to AxYZ?

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Q: Find the of Integ ration f(u)= tanu + Cos 2u. %3D

A: Given information is :

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

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Q: Suppose you want to prove that ARST Theorem. If you know that ZR = LX, what else do you need to…

A: In ∆RST  &  ∆XYZ, ∠R≅∠X.

Q: Derive the third order dervitive formula at x = x, by using Newton's forward differences

A: Consider the function y=fx which is tabulated for the values xi=x0+ih, i=0,1,2,.....,n. Suppose that…

Q: Determine the constants a and b such that                                                       sin…

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Q: Suppose X1, ..., Xn are iid with PDF f (x | 0) = 40ªx-5. x > 0, where 0 > 0. Find the method of…

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Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x"-1 sin x…

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Q: Siny+ tany siny %3D 1+ secy

A: Let's find.

Q: Find the value of the definite integrallo 2 cos ( x ) dx given that the antiderivative for the…

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Q: Use the methods of (1) left Riemann sum, (2) right Riemann sum, (3) trapezoidal rule, (4) parabolic…

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: By Cauchy's integral formula show that, Se" esin e -2n cos(cose) de = 2n; "esine sin(cose) de = 0 0,

A: Cauchy's integral formula : Let U be an open subset of the complex plane C, and suppose the closed…

Q: Use geometry to calculate (without integrating): o V16 – x2 dx Note that f (x) = v16 – x² is the top…

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Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x + 5…

A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

Q: Find the Integration of: f(3sin t + esin ty cost dt In 3

A: we have to integrate the following

Q: Derive the third order dervitive formula at x = x, by using Newton's forward differences.

A: To find dydx, differentiate the Newton's forward difference interpolation formula with respect to p,…

Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

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Q: Evaluate the integral. TC cos(x) sinh(x) dx

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Q: By using Beta function, the integral I tan(0) d0 is

A: To find value of integral∫0π2tanθ3dθ by using Beta function. Bm,n=ΓmΓnΓm+n…

Q: Find the approximation of the integral. 1= [e*dx Using Romberg's rule derived from Trapezoidal rule…

A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. .......Integrate f over the given interval of x, using…

A: Solution:

Q: Q! O show th at [x sin'x + V1-x²] = sin'x sin x

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Q: Use the tabular method to evaluate the integral |(* + 2x – 1) cos(4x)dx

A: Given:∫(x3+2x-1)cos(4x)dx

Q: The value of integral cos (1+x) d, n= 4 by Trapezoidal rule is (up to 4 decimal digit) Answer:

A: The trapezoidal rule can be used to calculate the integral numerically. The formula for the…

Q: make the given substitutions to evaluate the indefiniteintegrals. ∫√x sin2 (x3/2 - 1) dx, u = x3/2 -…

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Q: Use Property 8 to estimate the value of the integral.

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Q: .Find the estimate for the root of f(x) = sin x + cos (x² + 1) – 1using Bisection methodx, = 1.5, X…

A: Solution

Q: Use Secant method with p, =1, p, =1.2 to find the root of f(x)= In x-cos x that is accurate to…

A: Consider the given function  f(x)=lnx-cosx with initial estimate  po=1  ,        p1=1.2

Q: Give an interval over which you could integrate to find the area of one leaf of the rose r = 2 sin…

A: r=2sin3θ

Q: 4. Use definition (not tables) of L {f(t)}= [ e"f(t)dt to find L{sin(2t)} . %3D

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Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is:

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Q: Evaluate the integral. arctan(5t) dt

A: Here we evaluate the integral∫ arc tan 5t dt

Q: If I, = [4t 1 applying the technique of successive tan" x dx , show that I, +I,2 п-2 n-1…

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Q: Evaluate the integral. ∫arctan 4t dt

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Q: I* cos z lim 1³+2

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Q: dt cos°(2 sin" 21)/1– 4r cos(2 sin2t

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Q: 2T COs x dx

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Q: Integrate by parts f(x)=sin4(x)cos3 (x) dx

A: Given the integral  I = ∫cos3(x) sin4(x) dx cos2(x)=1−sin2(x) I = =∫cos(x)(−sin4(x)(sin2(x)−1)) dx…

Q: The actual error of the approximation of I = x² sin (x³) dx using composite Simpson's rule with n=4…

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Q: find the intergral of f(x) = sin(x) + cos(2x) on the interval [0,pi]

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Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson's 3/8 rule with (n₂ = 3) to estimate tan-¹(2).…

A: We have to estimate the given function.

Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x +…

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Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…