Estimate x using the trapezoid rule withn=4 a. Type equation here. Redo 9 using Simpson's rule. a. Type equation here.

Q: Z is the midpoint of VY and X is the midpoint of WY. If VW = s + 47 and XZ = s, what is the value of…

A: Given,          Z is the midpoint of VY¯ and X is the midpoint of WY¯ .           VW=s+47 and XZ=x…

Q: What is t' (x) if t(x) = ? ez

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Q: Trapezoid JKLM is shown below. y 4 К (2, 3) L (4, 3) 1 (1 1) M(5 1) 3. 2.

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Q: So, which of the following is the solution functiony(t) ? a) y(t)= sinh2t = e* %3D b) y(t) = sin2t –…

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Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule t 10 In(x) dx,n = 6

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Q: Let X; = tB¡ B,ds. | Is (X,)r20 a F - martingale?

A: Consider the given process:        Xt=tBt-∫0tBsds

Q: Find the length of the curve y = V4t2 – 1 dt, 1<x<2 O 3 O 8 O 104 3. O 15

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Q: Let w = x? dx + y? z² dydz. Find dw.

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Q: 5. Show that T = + y? satisfies the equation T + Tyy = T³

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Q: Find the family of oblique trajectories that intersect the family of the paraboles y = Cx at angle e…

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Q: esing pyphagoras th, Diff wt to t 2xda +rydy 20 at da dt az3 m

A: Apologies for the inconvenience.   Let, x = the distance from the wall. y = the height of the top of…

Q: FIND 2 DIFFERENT (LINEARLY INDE PENDENT) POR THE D.E. SOLUTIONS y"_x² y'- 3xy = o 2.

A: The linear homogeneous ordinary differential equation has the form pxy'' +qxy' +rxy=0. If the…

Q: Find the DE by eliminating the arbitrary constant  y = A+ bex

A: Given equation  y=A+be^x Where A &amp; b are arbitrary constant.

Q: use the trapezoidal rule to approximate use n=6 and h=1

A:

Q: Find he value of ds/du at u = 2 if s t2 + 5t and t (u? + 2u)/s %3D

A: Here, s=t2+5t and t=u2+2u13 So, s is a function t and t is a function of u. At u=2, t=(4+4)13=813=2

Q: Evalwate f, the inaicated point. (Y.y) and Fy y,y) CY.y) at 3. at (l,3)

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Q: Evaluate e*y dx dy by using trapezoidal and Simpson's rules.

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Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: Find the length of the curve. y = 2 – 4x, 1<a< 3 O 54 3V17 O 17 O 2y17

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Q: e) Use (; a²p Find the value of Vm at which both of these deriva- T to find aVm tives are zero.

A: I will present e bit for u in the last step....inorder to show u the steps clearly of e bit , I have…

Q: 4. Determine the c, and c2 so that the y(x) = c,e-* + cze8x + sinx that will satisfy the initial…

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Q: Cosot tunpt H %3D then G)= 22

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Q: ) Find the gavea d the rgion enclased by the line x-In3 and the curves y= ex and y=ex

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Q: H.W : Use the Trapezoidal Rule with n=6 to approximate. Here f(x)=sin2x,23D0,b=r.

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Q: Let z be a constant. Find the y" if y = v1 + 2zt + 5z't

A: Let z be a constant  To find y''if y=1+2zt+5z2t3

Q: f (x) = 0, %3D pendently selected, find the E

A: The number of sample is n=4. a. The probability of impurity weights exceeds 0.5 is,…

Q: express in the form y = f (x) by eliminating the parameter x =  e−2t , y = 6e4t

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Q: Classify the y'+y enx=0 dlifferantial equeltion dnd Pind its generdl solvtion.

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Q: Find the length of the curve y = V- from z =1 to r = e. 3

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Q: Find the length of the curve y = S Vcos t dt, 0 <x<n.

A: Given; The curve y=∫0xcost dt,      0≤x≤π .

Q: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: The length of the curve y = (2+ 2x )3/2 between x=0 and x=2 is O 41/3 O 45/2 O 43/2 O 47/3 49/6 ООО…

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Q: What is the relationship between ZW and ZX? 3,

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Q: Find y Ly imelicit differen -tiation, VスナUゾ 21

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Q: (a) Check Y (t) for stationarity (b) Check Y (t) for ergodicity.

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Q: A straight-line fit y3 = e12), could be obtained with:

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Q: H.W/ A/ Find e* dr approximately using the Trapezoidal rule with n 10.

A: Given integration is ∫13ex2dx here a=1, b=3 and n=10 It means [1,3] is divided into 10 subinterval.…

Q: ,use the linearity of L   determine L[f]. Q. f(t)=sinh bt, where b is constant.

A: Given, f(t)=sinh(bt), where b is constant To determine L[f].

Q: Use L and f' to solue ťtzyz fit), y0=5,where (2, 2)

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Q: Find he value of ds/du at u = 2 if s t2 + 5t and t = (u? + 2u)

A: ds/du=9/2

Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

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Q: Find dy/dr if y = r In(x). Answer:

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Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle e…

A: The answer is given below:

Q: I = 4t? dt J2

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Q: For x=In /t y=2, find y" when

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Q: draw the slope field for y' = x² – y², then use it to sketch three solution curves. %|

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Q: A researcher is nunning a simulation of an upward rocket to study the upward velocity of the rocket…

A: v = ulnmomo-qt -gtv=upward velocity 680ms                                u=fuel expelling velocity…

Q: in the form u = Rcos (wot-6). √3 sint u=-cost + V

A: The given problem is to write the given trigonometric term in terms of single term as u =…

Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.