6. Prove or provide a counter example for the following: (a) (AU B)nC = (AnC)U(BnC) (b) (An B)' = A' UB' (c) AAB = AUB if and only if A n B = 0

Q: 10 of 17 If y(t)+(t-r)y(r)dr=t, then y(t)= Su-nyndr3Dt,

A: Convolution Theorem: The Laplace Transform of the convolution of f(t) and g(t) is:…

Q: 12 3. If u lx + my, v = mx-ly, show that ди 4 + m

A:

Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

A:

Q: Solve the following first-order linear DE's. y' + (cotx)y = xcscx, y = 1

A: we have to find the general solution

Q: 4/ur grans funthon y"-Uy't3y = et

A:

Q: Hor what salue of e dois th. a tollowng matrex haue an Tnverse Q. 2. 2.

A:

Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

A:

Q: 3 Find C at any time7 2l/min SIN SIO 6l /min 8 elmin C NI8 100 Pure waley

A:

Q: now tha 4.31) and that cov(y-ΣΣ) Σ- as in 4.32). – E,. x) = ΣΣΣ as in (4.32). %3D

A: E(y-∑yx∑xxx) = E(y)-∑yx∑xxE(x) = μy-∑yx∑xx μx AS E(y) = μy E(x)=μx ∑yx is the covariance marix…

Q: 7 y=tanx show thats y" = -2Siny cosy 1f y=e Snbx show that:

A: Dear Student, according to the Bartleby guidelines, we can answer only first question if multiple…

Q: 7. Solve the following first-order linear DE's. y' + (cotx)y = xcscx, ) = 1

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: - check the exi's tence of limol of the Lunetiom 41n at X= 1 %3D 2X+/ こ Xラ-3

A: To check: The existence of the limit of the function. Given: The function is fx=2x+1     -1≤x≤1x22-3…

Q: 12, Show that ()() = (OC)- n-m' %3D 13. Show thet (A)

A:

Q: 6. If y = In(r+ 1) In z then what is dy/dr? %3D

A:

Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: 1- Two vecters n'and mª anl Said to be orthogenal if n'entzo T b. F a.

A: The given statement is: Two vectors n and m are said to be orthogonal if nxm=0 To determine whether…

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A:

Q: if JERLA.b] and it hex)- J(x). except for finite mumber of Paint in Cab] then that he Rlab] prove.…

A: if g ∈R[a,b] and if h(x) = g(x) except for a finite number of points in [a,b] then prove that h…

Q: Prove by mathematical induetion. Ine I+2 +2+2 +2° = 2.

A:

Q: 2) Eliminate the arbitrary enstant, 4 y= x*+ Cix + Cz e-X

A: Given problem:- Eliminate the arbitrary constants. of y= x² + C₁x + C₂ e-x

Q: af af дх ду af az and of. HINT [See Exam Find 24 fx, у, 2) : x² + y2 + z2 af af ду af az %3D

A:

Q: If b is dviisible by a (a|b) and b in different than 0 then |a| is less or equal than |b|

A: The given statement means the following.

Q: (2) O show that you Y2,43, and Yu are solutians to NOTE : Geueral Solufion

A: Thanks for the question :)And your upvote will be really appreciable ;) Solution is provided below,…

Q: Verify Young's Theorem z = In(2x + y) -

A:

Q: Give a clear and detailed solution of the intergral of e^-ct/m 2)

A: You want intergral of e^-ct/m. I am assumig the variable of integration is "t". That is, the task in…

Q: Obtain the general soluti d²y 1. 7- y = 10sin²x

A: Given: d2ydx2-y=10 sin2(x)

Q: 13. - (In t ² )º t dt

A:

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: prove: sE121y |Re(z)+| Imcz)l

A:

Q: Show that Z, dv=2010 %3D if B= 2) : -1 Śn s3, ISySY,e

A:

Q: Is there a way to solve this w/o using L'Hospital's rule?

A: Solution

Q: 5. It is desired to divert 5.1 m'/s water from a pool whose water surface elevation is 45 m, to an…

A: according to question ∆H=45-42m      =3m length of concrete culvert L=8 m now, find the slope S=∆HL…

Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: dT 4 dp 0; pdT T = To when p= Po dp Po e (T-To) O Option 5 L = e- (T-To) Po O Option 2 -0.5 (To-T)…

A:

Q: 16) 1. ZDX 2. -X Show Your Work Valid Invalid

A: We have: Z⊃X~X ∴~Z    This can be written as Z⊃X∧~X⊃~Z  Here, p⊃q means "if p then q" This argument…

Q: 12 २ (४) = dt | २स Prove !- \) ২-০০) = २(-०० ) 3D \

A: Given that Qx=12π∫x∞e-t22dtTo prove:1. Q-∞=12. Q-x=1-QxSolution:we know that ∫-∞∞e-x2dx=π       ...…

Q: 10:29 ll LTE O True or False 11. If two figures are congruent there is always just one way to…

A: Statement is given  We have to define it is true or not

Q: 5. Show that xZx + yZry = yezy if z= xy + y In xy

A:

Q: 6. Which of the followg quti dy (a) de dy (b) de () +2ry- (e) (4) Al of the above

A: It is given that There are four differential equations option.

Q: -64- Eke n Calcul afe th udlue of Z.Z ?

A: according to company rule we answer only first question and rest can be reposted.

Q: 7) [[3embch5y] dvl [jel*5) dy] „In[sec h 5y]

A: Using rule of logarithm & integration formula of sech(x)

Q: A.o/ prove haT cosh(zi42e)=Coshzcoshai+sinh2,Suhze

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Find y' in y = (x³ 3x²(x²+e) x³ +3 A. y' = B. y' = C. y' = +3)(x²+e) +7x6 In (2³ + 3) +7x6 (x³ + 3)…

A: Understanding of derivative when function is there in power of any function.

Q: lestion 25 Consider the following IVP: y" + 3y' + 2y = 12x?; y(0) = a, y'(0) = b

A:

Q: pes of animals are treated by at least on r. Scott, and Dr. Baker)?

A:

Q: See image below.

A: Given that the tangent line touches the curve y = f(x) at (4, 3) passes through the point (0, 2).…

Q: 5) why is x3- 3x +I X +2 Conti nuous (0,00) on where is it discontinuous?

A:

Q: Show that lm Casy -1 CoSy-1

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.