6Let w7 d x)t 2 Find nd simplity the follwing Hinti e aneers from t

Q: Derive and use the estimate 800 |u (x, t)| < 1 -7²t/10 re (2k + 1)* k=0

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Q: Q Find the Probabi litty of finding aclosed patht f m if the probebiltyof Switching onf f •f

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Q: EX. Use Euler's method (moditied) t appro y' = x+y for y C1) = 1 ; h =0.1,13XL2 Ư the açcuracy of E…

A: According to the given information it is required to approximate y'=x2+y for y(1)=1, h=0.1, 1≤x≤2

Q: Solve by using Separution of Vadiyble Methol Conetition Sntefing the condibtton T>o as t->0 as T=0…

A: Given         ∂T∂t=∂2T∂x2                   (1) Satisfying the boundary conditions   T→0 as t→∞…

Q: 3. Evaluate xdV, where E lies between the spheres p 1 and p 3 and above the cone

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Q: EXomple CHa): let X aned Y ave Cag. V'S with joind to e-w G Find the Value ofc. Q Finel…

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Q: OMNPQ, with T the midpoint of MN and S the midpoint of QP AQMS = ANPT and MSPT is a O Given: Prove:…

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Q: Find y" by imprcit differen fia fên. Simpliey unenoven Po Ssiole

A: Given:- x2 + 9y2 =9  To find:- y'' of given equation

Q: 5.2 Q3: By using Trapezoidal rule find I | In xdx , where n=6.

A: The objective is to find the integration of the given function in the interval [4,5.2] by using…

Q: Q6. Given M = {(x, y), 1 < a² + y² < 4} c R². (a) Determine dM and aM. (b) Is M connected? Pathwise…

A: On the set M, we have to find the following results.

Q: Find length of the cardioid r-a03from 0 0 to 0 t %3D

A: To find Length of cardioid r=aθ3  where θ=0 to θ=π

Q: B. Obtain PDE by eliminating the arbitrary functionsfrom the following; 2. Ix + my + nz = Ø (x2 + y?…

A: Partial differential equation by eliminating arbitrary function

Q: Which of these are closed regions? D.|Arg z|1 F.-1<I'm z<=1

A: D. 1)arg(z) is the angle between the line joining your point z=a+ibz=a+ib and the origin, in the…

Q: Let f(x, y) = 9e2xy what is fxyx (x, y) =? %3D Select one: O a. 72ye2xy + 72xy²e2xy O b. 36хуе2у +…

A: Given: f(x,y)=9 e2xy ; To find the value of fxyx(x,y)=?

Q: R Given: m ZRTS = 90; M MN is the 1 bisector of TS. Prove: TM is a median. T. N

A: In a triangle RTS , angle of RTS is 90 and MN↔ is perpendicular bisector of TS Midsegment Theorem:…

Q: I Find for each of the following. keving your anwer in terms of the parameter . 2r, y- 2

A: We have to find dydx for the following...

Q: (b) Let X = {A E Mat2(R) : A is upper triangular} and let Y = {A € Mat2(R) : A is lower triangular}.…

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Q: 2. Suppene F=Q . L the set 4 2 3 4 lnianly ? why any o? nhar happeno is F=Zs ? nidependent so? rhar

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Q: 25. Which of the following is the answer for secx = V2 A. E + 2nk|k E Z}U {+ 2rnk|k € Z} 3 B. G+…

A: We will solve the problem

Q: Hewin If Z =R Cxxy]:and u=x-yg V=x²-y 그를 + show that

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Q: IS T-dist prove o E(T)=0 QvarしT)=て %3D V-2

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Q: Q.5 Use both trapezoidal and Simpson's Rule to evaluate |(² +1)° dxby taking n=4.

A: We have to find integral of given function by using Trapezoidal Rule and Simpson's Rule.

Q: 3. Show that S4 has the presentation (x, y|x* = y² = (xy) = 1). %3D

A: To show: S4 has the presentation x,y| x4=y2=(xy)3=1

Q: Compute the length of the curve r(t) = (21, In(t), r?) over the interval 1 <t < 9. (Use symbolic…

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Q: 13. Estimate fcos (x²) dx using (a) the Trapezoidal Rule and (b) the Midpoint Rule, each with 0 n =…

A: (a) Estimate by Trapezoidel Rule for n=4in this case f(x) = cosx2 , a= 0 , b = 1 , n = 4  and ∆x =…

Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: Find length of the cardioid r=a0³from 0 = 0 to 0 = n %3D

A: Length of the cadioid is given by below formulaLength = ∫0πaθ3dθ

Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

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Q: let x be have P.dif 0 < x <3 f(x)= ={th find The U.b. of P(IX-M73) and find The L. b.

A: Please see below

Q: Q5: For which values of z is w =1/(z - i), defined? For these values obtain u and v and evaluate w…

A: Given that: w=1z-i, z=1-2i

Q: EX: Find the Z. T. of X(X) = cas wok u(k) Soin

A: Z transform of the function

Q: 1 f f(x) = : R → R, Vx2 – 4 At how many different integer points x is discontinuous? 25 - O A) 3 O…

A: We have f(x) = 1x2-4Clearly f(x) assumes real values for all real values for all x except for the…

Q: Fourth question: r = 7| , = xi + 4yj- 2zk Let it be V(6r), v²(7r) find all of

A: According to question,r = r→,andr→ = xi + 4yj- 2zk

Q: Decide if the statement is True or False. Justify your ans why not, and give an…

A: a) The poset (P(Z), ⊆)

Q: Q6. Given M = {(x, y), 1 < x² + y² < 4} C R². (a) Determine dM and aM. (b) Is M connected? Pathwise…

A: Given that M={(x,y),1≤x2+y2&lt;4} (a) Given M is a region enclosed between open circle of radius 2…

Q: fined the conter, fuci,vedices and ecentrici ty for fhe folowing equetins! I x+uy-4x -8y +4=0…

A: Let us consider the equation of ellipse (x-h)2a2+y-k2b2=1 Center is (h, k) vertices is h±a,k Foci…

Q: df Let f(x,y,z)=xy+z?, x =s², y =2rs, z =r?. Find when S =1 and r=5. ds

A: Given that f(x,y,z)=xy+z^2 ,x=s^2 , y=2rs ,z=r^2 We have to find ∂f∂swhen s=1 and r=5

Q: Compute the length of the curve r(t) = (21, In(?), r²) over the interval 1 < t < 7. (Use symbolic…

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Q: Q5/ If w = f(x,y),x = rcos0,y = rsin0 show that: af af 5² + 1 dw Əw. -)² + ar r2 a0 дө

A: The chain rule can be used to calculate the derivative of the complex functions. The function which…

Q: Q. Fosm a Paitial Digferential puation constoht Methad q elimination of elimnalan f Arbltiay Con Z=1

A: The given equation is        xa+yb+zc=1 ...............(1)   Let x, y are independent variables and…

Q: Q4. Find guerel polution of following systens uning either method' of undetermind coefticients or…

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Q: a the diagram, PU||QT, Ì = 42°, RQS = 82°, = v, UPT =r and QPT = x+40°. Prove that PT|QS. %3D P…

A: Given: PU||QT Concept: Pair of interior angles on the same side of the transversal are supplementary

Q: Write a in the fom a = a7T + ax N att 0 for R(t) =t?i+ (t+);+(t -)*

A: We have given R(t)=t2i+(t+13t2)j+(t-13t2)kV(t)=derivative of…

Q: 03) find the ax en the sl abetwed wol y=J2-X, and y= 0

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Q: Let *- y= ÿ.z=0 and x ỹxz= V3 where x,y,ZER'. Which of the followin. 2 can be the value of X Z? V3…

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Q: 5. Given: m|| n with t a transversal cutting both of them. Use two-column proof. Prove: a. Z1= < 4…

A: We have to prove using two column method in which 1st column have statement and 3nd have their…

Q: Let be Z= ax? yf +bx²y³ 9 and b que cors P is a pant givon by (-1,-1) qnd we Anaw dz (P) = -2 , &르…

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Q: II. Let U = R, { x € R | 26x + 25x = 0}, J = { x €R | |4x + 2| > 10 } and K = { x € R | x? – 3x – 4…

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