Consider A) "sin(In z) B) dz In(z) hint: Taylor D) w/ E) none of these

Q: If sinr = In y, show that dyOUTM dr OUTMO (1--- (1– 2) dy = y. dr

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Q: z = tan¯1(4 – j7)

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Q: Aro/ prove JhaT cosh(?14z)=coshzi cosh2.+ Sinh2,Sinhze Hiw/ It isinh Z = siniz, prove That: %3D…

A: Note: As per bartleby guidelines for more than one questions asked only one question is to be…

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

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Q: dy is If y = In then cosh z

A: Given,          y=lnxcoshx

Q: 10 Use the fundamental theorem to evaluate the following integras 1+2i (a) cos3z dz S ze*, (b) (c) J…

A: Dear Learner,we can solve only three subparts as we are following Bartlbey Experts Guildlines to…

Q: The suitable substitution to evaluate the integral /tan°(2x) dx is cos“(2x) O u= tan(2x) O u=…

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

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

Q: 2, Sove the Following Riccati equâtion dy 2008?x- Sin?x +y? %3D 2 cosX

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Q: Since Cov (X, Y) = E [X, Y] -E [X] E [Y]. Obtain Cov (Yi, BO)

A: From the given information, Consider, the regression equation be assumed as given below:…

Q: i) um asinx-sin2z ,u fünute, fünd the vaue the uimit. tana ofa and

A: Now, the limit is finite given so, the above must be 00form So,  a cos0-2cos0=0⇒a-2=0⇒a=2

Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

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Q: Use the definition. that sinz •prove Z = UJZ %3D

A: Using definition of derivatives.

Q: Use the fundamental theorem of calculus part 2 to evaluate the 3 integral: (8 sin x) dx. Noto: Round…

A: Our Aim is to evaluate the integral given below:-∫π/4π/3 (8 sin x) dx -(i) using Fundamental Theorem…

Q: Evaluate the integral ſſ /ydA, where T- triangle with vertices (1,0), (0, 1), (1, 1).

A: Let us consider the double integral  I=∫ab∫f(x)g(x) f(x,y) dydx    or I=∫ab∫f(y)g(y) f(x,y) dxdy…

Q: O! Find tue indefinite integrel by q meleing tue febstelion d=4 Sin o. 2 *7 16-x"

A: To determine: by substituting x = 4sinθ

Q: 21. Prove that lsio rol ylanoti (i) Res (tan z, x/2) – – 1 1-cos z (ii) Res 12

A: The solution is given as

Q: Evaluate. de In(sin æ)] sin z cos z eCoS Z coS z COS T sin z esin z

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Q: Discuss the cosets of { (x, y) | x, y E R, x = y } in (R × R, +).

A: {(x,y) / x,y∈ℝ , x=y} in (ℝ×ℝ,+)

Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

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

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Q: Evaluate the iterated integral. "TU 2 √4-22 ²² z sin(x) dy dz dx

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Q: Gren thint sin (A+i6) = xtiy, 28 Prove that, 9父+ =1 snh'B 1) x essec?A -y' sec'A =1

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Q: By the samc way, prove that g 7 sinw.k MUIS Z N-27 cesW. +1

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

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Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where u> |z| > 0

A: Prove,∫z=1dzz2 sinh z=-πi3 ∫z=1dzz2 sinh z=∫z=1fz dz .........equation 1 fz=1z2 sinh z , 0<z<π…

Q: Let - (sin x cos y, COS I sin y, In). Compute div i

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Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

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Q: Evaluate the following integral JI (1 – (x + y))dA where T is the triangle with vertices (0, 0), (1,…

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Q: Complete the two-column proof. Given: ZB = ZR, ZBPC = ZRCP Prove: ABPC =ARCP R Statements Reasons I

A: Answer and explanation is given below...

Q: ) Let Z= re q iy be a complex mumber Such that cosh Z+o. then Re (tanh z) is equal to Sin a cesn

A: In the given question we have to find the real part of tanhz and and also check it that is it equal…

Q: Compute algebraically the resultant of the following complanar displacements: 100 N at 30°, 141.4 N…

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Q: Classify the Stries as nbsolurehy linvergen ti Condibinally lonvergent, divergent 18 K Sin

A: First we  recall some definition-1)  p-test for convergence of series ∑k=1∞1(ak±b)p :     A series…

Q: The integral of the right hand member of the first order LDE A B C с D -2sin³0 3 COS 2 2sin³0 3 sin…

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Q: The suitable substitution to evaluate the integral [V cof (2x) sin (2x) dx is u = cof(2x) u =…

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Q: D. If z = In(x – y) + tan(x + y), show that Z = Z y XX

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Q: Prove the following hyperbolic trig identity. cosh(x + y) = cosh(x) cosh(y) + sinh(x) sinh(y).

A: cosh(x+y)=cosh(x)cosh(y)+sinh(x)sinh(y)

Q: Show that J, (z cos0)d0 = - R/2 os e)de = 1-cos z %3D 21

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Q: The suitable substitution to evaluate the integral [V tan (2x) dx is cos (2x) O u= sec(2x) u =…

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Q: use the definition, prove that d sin z = cOs z dz

A: Topic = Derivative

Q: Let fln) = e cosx, sx %3D Express your answers in exact form.

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Q: If z = exy where x = In(u + v) and y = sin(u-v), find az and az du

A: We use the partial derivatives and chain rule of differentiation to answer the given question.

Q: Prove that d/dz sin(z) = cos(z) using Cauchy-Riemann equations

A: Cauchy-Riemann Equation- If f(z)=u(x, y)+i v(x,  y) is analytic, then In particular, These…

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

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Q: Find all Solotioms Cin radins) to the eguotion 2 Sin X+V3= o

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Q: 15. are tag z dr z arc tag z - In /1 + z² + c – In /1 + z² + C %3D

A: By using integration by part

Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…

Q: Let = (sin x cos y, cos I sin y, In z).- Compute div i %3D

A: Given,          v→ =  sinxcosy , cosxsiny , lnz

Q: Prove,J w' Sin wx du %3D COSZ 2

A: