2uppore that tuo - dimensional, contiruous Mandom uariable (x,4) fa's yont" P•d.«b. gien by : , elsewhere us woify trat c ind P (o

Q: a) Demonstrate Gra phically the contimuity /Discontinuity of the tunction fx)- * ,0くxく」 1. 1+x)…

A: Authoring guidelines:…

Q: Iff: [a,b] R is bounded and has only a finit number of discontinuous points, then f is Riemann…

A:

Q: Prove that cosh-z = In (z + vz? - 1) %3D

A:

Q: dy is If y = In then cosh z

A: Given,          y=lnxcoshx

Q: Show that the following line integral is path independer (3,5) y² %3D cosh( )(10xdx +6ydy) (0,0) 3

A:

Q: b) Estimate the integral esindx using composite traperoidal rule with h= 0.25.

A:

Q: Prove That:- o sinhz= loy (Z+lz*+l )

A: To prove, sinh-1z=logz+z2+1     Lets consider, y=sinh-1z…

Q: Compute the definite integral as the limit of Riemann sums, Verify by FTC, and using Desmos. 1) y =…

A: By Reimann sum, ∆x=b-an=4-0n=4n Again,  xi=0+i·∆x=4in Now,…

Q: 4. If R is the total resistance of three resistors, connected in parallel, with resistances R, R,,…

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

Q: Compute the definite integral as the limit of Riemann sums, Verify by FTC, and using Desmos. 19) y =…

A:

Q: A): Let Using only the defination of xate of chamge in tems of limit, Compute dy the defination of…

A:

Q: Find antideriuative Flx) of the an flx) = _8 sinx 13 + COSX functian such that FlO) = 1 %3D %3D

A:

Q: 2. Prove or disprove that Z, xZ, is integral domain.

A:

Q: Ex(ia)g prove or dis prove that Ris equivalance relation on x iff Rtis equivalene relakion ony

A:

Q: and let ah -(-1'I Let In tan (a) for n = 0,1, 2 Intz 1) Show that In + Io+ り+! (-1)" for nal an-…

A:

Q: Which substitution is needed to evaluate the integral S tan* x sec² x dx =? u = tan* x, du = sec? x…

A:

Q: 5) Set the iterated double integral ļ) dydx メモービ テ as Jady up

A: Please see the below explanation.

Q: . Use Taylor's neries, to prove that ein z tan (x+ h)3tan" % + (h sin z). sin 3z sin 2z + (h sin zj…

A:

Q: Find the value of c and they give an interval that satisfies the mean value theorem of integrals

A:

Q: Solve using horizantal Slide EX Evaluat..f.x.dA.whak.R.a.the.sgen.in.the figt.…

A: ∫∫R f(x,y) dA= ∫∫R f(x,y) dxdy =∫∫R f(x,y) dydx

Q: Cannot solve

A: Multiplying and dividing first term by secx and second term by tanx of left hand side of equation ,…

Q: Let S be the portion of the cylinder z = 1 − x2, in the first octant and between the planes y = 0…

A: We will find out the required value of a.

Q: 2.Prove that L (sinwt) %3D s2+w?

A:

Q: Find the integration of S ecosx dx using Trapezoidal and Simpson's Rules

A:

Q: Show Z=arctan(y/x) satisfies Zxx+Zyy=0.

A:

Q: If f: [a, b] - R is bounded and has only a finit number of discontinuous points, then f is Riemann…

A:

Q: sample of size n from N CO, a2) Then show That * Ex;2 is an Theorem- a X, - - be a yandom unbaised…

A:

Q: ae e drea under the curvé y=*from2-2to2 using a Rightt Endpoint approximation with 6 subdivisions..

A:

Q: Set up UP the integrel the Pegioni Th bounded 2x2 and y =l+ x F(x,y) dA in by: y= 2x? 2. 4.

A:

Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: evaluate the arca of He reginn bounded below by and y= aboue by y=X

A:

Q: 3. Evaluate JIJ 62² dV where G is bounded by x + 2y + 4z = 8 in the first octant.

A:

Q: 2 Evalu ate the fllowing integral - R Is the regiovi be undéd by the grapis x:2, y= x-5, and…

A: We will evaluate the required value.

Q: The volume of a section in a thread is given by=V = 4Sinx(1 + Cosx). What is the value of x that…

A:

Q: thゃト IF Sequieree is divergent to prove THEN bounded below. it is

A:

Q: 2,- Show Continuous at x =0 me the follewing functron rot fex) = Ix/ or he

A:

Q: J uore program Use a soft groping of ality aith motrix copobilities to'find the eligenualves the…

A: For any matrix, A , the eigen values are calculated by solving the equation, det(A-λI)=0 . Here , I…

Q: 7. Prove that the SolutmM of y + y = o is B sinx (hint y= Xu) by using Bessel's Functron definstian…

A:

Q: let X = * = zrs, find 22u in term f partial deriva bives

A:

Q: Show that the following line integral is path independent an (3, 2) S cosh(+ X (0,0) (8xdx+6ydy)

A:

Q: use Greens Theorem to evaluate . cosy dx + (xy- x siny)dy Ewhere C is the bounday of the y Jx,…

A: We have to evaluate given integral using Green's theorem.

Q: use the limit of the Riemann Sum to find exacct ared under the curve. flx) = 4 x [2,5]

A:

Q: let 9: R-R be given by grs) - Sin (는) %3D %3D dis prove that se second hind has prove of dis…

A:

Q: Q4: State the Fundamental Theorem of Independent of Path and Morera's Theorem. Why can't apply these…

A:

Q: Prove that tan'z= leto 1/2 in (1+2) tan't z • tanw=Z Z = Sinw cosw

A:

Q: (Compute Sc (-3y+ony Sin(3))dxt (5x²-(ye)du Where C is a Simple Clased cUne in the plane oriented…

A:

Q: use the funda men tal Theorem of Culculus to find the under Curue of 2. y = -xFl0 x between x = 3…

A:

Q: 2)Evaluate er dA , Ris bounded by y = x2,y 1 3)Evaluate I| Vy2 + 1dA , Ris bounded by x = 4 - y? ,x…

A:

Q: @ Hiw/ prove that cosiz=coshz @ Cosh'z @ 1- Tanhz - Sechz

A: As per Bartleby's expert answering policy, we can answer only one question with a maximum of three…