Define lopico, ) → IR and exp:IR →(0,00). And then show that and exp'ex)=explx).

Q: Given: WZ 1 bis. XY Prove: AWXY is isosceles. (Hint: This proof can be written in three steps by…

A: 2. given  WZ↔ ⊥bis XY¯ as WZ is bisector of XY XZ=ZY......(1)

Q: 5. Prove that So*(y – 0)dydr =

A:

Q: Find the Leplace bransform. of Hhe fure tion ESinut octca to biven that

A: Laplace transform of periodic function: The Laplace transform of a periodic function f(t) of period…

Q: Give the condition which ensure that Je-| < 1 where z E C.

A:

Q: XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1).  Which of the following can be used to prove that…

A: The answer is given as follows :

Q: 1 Using Convolution theorem, find (i) L (s+a)(s+b),

A:

Q: every vertor (en Sination of Hhe vertars (e, 2) and {-2,1)? ☺ Is linem reitars Provida why Jatailad…

A: Solution is given by using linear independence of vectors as follows :

Q: alue of the pur C: |z| = (:-1)(z-

A:

Q: matoix Such that show that Let is Then detx = tt mxn

A:

Q: Find the fowien senies fon | X), -T<X <A

A:

Q: Let R = [0, 1] × [0, 1] . Est each with at least six rectan IR 6(x + y) dA 2

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

Q: 2), Compute SE. di where Fュく-,) C is s shown

A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

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: y Verify Euler's theorem for u = x' In

A:

Q: (b) Compute r if: arctan r + arctan 1 = 2 ( arctan z arctan

A: tan-1x+tan-11=2tan-1x-tan-113

Q: Find the Avorare valne of Hhe famdtiun en the interal [ 0,4J VI+ 2x

A: Average value of the function on a given interval is 1/(b-a) integration of a given funtion…

Q: 2. (– 13 + 3i)31

A:

Q: (o, 1,) 1. find th directional denivatve in the dire chons of at 2 Gve inter pretahon of amp uted…

A:

Q: If y = xsinx then prove that y''+y=2cosx

A:

Q: et X~U([-, 1) and let y = tan(r), show that y Cauchy(0, 1)

A: # using Jacobian transformation we have proved that y=tanx follow Cauchy distribution (0, 1)

Q: 2.Prove that I (sinwt) : s2+w?

A:

Q: △XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1).  Which of the following can be used to prove…

A: Given △XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1)

Q: Csc? %3D 2cotx

A: csc2x2cotx=csc2x

Q: lar, let m = 2 and n e of A and B such that

A:

Q: What part is needed to prove the triangeis are congruent by SAS?

A: Choose the correct option.

Q: Exercise.2 Prove that cos-1 z =- In(z ± Vz? – 1)

A: The given problem is to prove the given inverse complex trigonometric identity. cos-1(z)=1/j…

Q: In R', the point (1, 1, 1) does not belong to the cylinder x + y = 2. Select one: True O False

A: Given problem:- In R³, the point (1, 1, 1) does not belong to the cylinder x² + y² = 2.  True  False

Q: The Position of by Patticle defined (4Sın TI ti+4costj + 6tK) Determine To magmtude of velouty and…

A:

Q: If x<y, prove that x<(x+y)/2<y?

A:

Q: ) Prove that sac"()/T sec

A:

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y3…

A:

Q: dual of c, is isometric to l'.

A:

Q: Let f lany) prove that' flany) di f feren tiable I5 not point lo,0) .

A: Let the function be fx,y=xy Note:  [ We can say that f is differentiable at (a,b) if f is…

Q: If (a + bx)e = x, prove that x’y, =(xy,-y)

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

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y4…

A:

Q: cos (o,+ O>)+ ì s:in (8,+Ə.)) Prove this kW- Mon 183O

A:

Q: /show that fo-1x is-Contindals everywhere.

A:

Q: Suppose you Know that tand 3/12. Vsing this infe, de tevmine cuhot quadiantdis in dnd Caliulate…

A:

Q: and are 2 soihions and w Cy,,Y2)(to)to what con conclude ? we

A:

Q: a) Suppose that you wish to prove that ARST = ASRV. Using the reason Identity, name one pair of…

A: Given: We wish to have the triangle RST and triangle RSV to be congruent.

Q: a²z If z = arctan ), find ( ay?

A: Given,           z=arctanyx= tan-1yxTo find           ∂2z∂x2+∂2z∂y2=?

Q: ion Prove that for

A:

Q: Using Eirjenvelue melthed envalie methed +2y dy ?a-2y 3 of

A: Given that, dxdt=-52x+2y   and dydt=34x-2y write in matrix form, x'y'=-52234-2xy for eigen values,…

Q: V- Assuming Cov(X, u) = 0 allows us to equate Ex û to zero. True or False? Explain.

A:

Q: 3 tari' (xty) , Prane that x2+ ydz Sen 2z be

A: We have z=tan-1x+yx-y This implies tanz=x+yx-y Let u=tanz Then we first need to find the degree of…

Q: Explain the fundamental theorem of albenra?

A: To explain: Fundamental theorem of Algebra

Q: Ihow do you bnd the imit of as x approaches 0?

A: The limit of x+1-1x as x approaches to 0

Q: d'y on of x

A: