show that the differential eguation is exact, then solre that method using 2 2 dy- x²-x+y? |

Q: Q2/ Prove that 1 dx = v2 Jo 1+sin(x)

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Q: Show complete solution. Expand, that is, perform the indicated operations on the differential…

A: We have to find out the operation

Q: Find the Undo pet CWor wa)or the form of a particular solution for the differential eguation:y…

A: Introduction: The method of the undetermined coefficient is a way to find the particular solution of…

Q: Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

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Q: Solve the following DEQ by separable method: dy (cos x + 1)( sin y – 1) dx

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

A: Given differential equation is y''+y'-2y=ex+sinxfind the general solution

Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: 3. (a) Compute ,12x – 1| dx in two ways. i. By using properties of the definite integral and the…

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Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: Find the differential dy of the given function. (Use "dx" for dx.) = 8x3/4 dy = %3D

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Q: Show that Ě = 3xyê+G)+2Ê is R3 and Pind Conservative a potential Ø Rar F. on

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Q: Prove that sinh−1 t = ln(t + √t2 + 1 ).

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Q: The velocity of a particle moving back and forth on a line isy = ds/dt = 6 sin 2t m/sec for all t.…

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Q: 10. Use differentials to estimate to estimate sin(46°). vZ(n+180) А. D. VZ(T+180) 360 180 В.…

A: Let y = sin (x)

Q: Use the modified Euler Method to solve the ODE = subject to y 1 when x 0 %3D dx 1+x on the interval…

A: To find y(0.3) by using the modified Euler's method.

Q: The suitable substitution to evaluate the integral V cos (2x) dx is COS

A: Given that:∫cos5(2x)csc3(2x)dx

Q: Use Secant method to to approximate the solution of f(r) = z+ cos z =0 accurate to within 10-3,…

A: The secant method is used to calculate the root of the function. The formula for the secant method…

Q: Find the value of dx (7x – 2)° If the integral diverges, give "oo" as your answer. -

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Q: Q4) A) Find by using chain rule if f = ( , u=-1, x=-1 dx ++1 B) Evaluate the following integral: V2…

A: Given f(u)=u-1u+12   , u=1x2-1    , x=-1

Q: a) For 0 ≤ x ≤ 1, show that < x². √2 + x b) Use the estimate in a) and integrate it to prove that…

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Q: Use the bise ction to approximate the solution of F(X)=Vx - cos X = 0 accurate to within 10 -3 on…

A: Bisection method: In order to find root of equation f(x)=0 in a,b such that f(a)f(b)&lt;0 Bisect the…

Q: dy dr

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Q: From the differential equati on by eliminating the arbitrary function ffrom xyz = f (x?+y'+z°).

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Q: Prove: ex. a. ſ csch x = In b. S sech x = 2 Arctan(e*) + c

A: a).  ∫cschx dx=∫2ex-e-x dx=∫2ex-1ex dx=∫2exex2-1 dx Put, ex=t⇒ex=dtdx⇒ex dx=dt Therefore, ∫cschx…

Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: In? (In(ax)) dx,a >0 -dr, a a. 2x In(ax)

A: You can solve this problem using the substitution method

Q: Ex. 2. Prove thät if two equal and perfectly elastic balls moving in the same direction collide…

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Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - dy -x-(x2+y²). sec.…

A: Please see the explanation below..

Q: Q1: Use Newton - Raphson method to estimate the 3 Voot of fcx) = x -X - 1, e mp loying an initial…

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Q: au Show that the local truncation error at the pint (ih,jh) of the Crank-Nikolson approximation to…

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Q: hD (Hint: E =eD and Sinh x: 2 Q3: Prove that 8 = 2Sinh %3D

A: We will prove the following result.

Q: Let y = tan(4r + 8). Find the differential dy when a = 3 and dæ = 0.1 Find the differential dy when…

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Q: dx J x2-4x+5

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

Q: Which integral 12 225-x¹+1 2 S√√2-√√225x4+1 dx So 9 is the arclength of the curve y = 5 x³ on the…

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Q: 2. u(x)= secx+à So u(t)dt.

A: Given integral Fredholm equation, ux=sec2x+λ∫01utdt To find the solution of this equation.

Q: Compute x² In a dx both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's 3/8…

A: For the solution follow the next steps.

Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: Find the value of the improper integral or state that it is divergent. (If it is divergent, enter…

A: We will calculate the definite integral using basic definite integral properties and if we get an…

Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

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Q: tanh (22) d) evalvare J seen 2 (2n ) e レッ using a substitution Suitable

A: To evaluate the given integral.

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y 2logy x %3D

A: we have ,  y=3sec3t and x=etan3t we have to prove that , dydx=(ln3)2·yx·logyx…

Q: (4z + 5)² tan zy= + dr Cos z

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Q: b) Use it in oonjunction with Simpson's 1/3 nule to integrate the same function for ive egmenta…

A: Introduction: Simpson's rule is a method to approximate a definite integral. The interval must be…

Q: how can i derive this equation in 3 D? *be aqy ay az at Əx

A: Taking heat in three dimensions (I) Net amount of heat conducted into dxdydz per unit time.…

Q: Find dy/dt. show all work y=cos(square root of 8t+12)

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x – sin xy; x = y = 2t t' Enter…

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Q: does not exist. (b) If u = x cos y+ye", where x=s+2r and y = st , prove that ди ди dt = (s – 21) (x²…

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Q: F (t)= 7tei+ sin²(2t)j – In (5t)k Vhat is F'(t)?

A: Here we apply detective.

Q: sin(20nnt) ass A: AS(t)ln:0dd En=1 %3D %3D1

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Q: Show complete solution Expand, that is, perform the indicated operations on the differential…

A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x