Evaluate. d [arctan a – In ¤] dæ 1 1+#? 1 sec2 x sec² ¤ 1-x²

Q: S (x, y) = sen (r² – 0²) + In(r® + 0), con Vr? + y? A r = = arctan

A: Given that, f(x, y)=sen2r2-θ2+lnrθ+θfor r=x2+y2and θ=arctanyx

Q: If x = t + 2 sin(at), y = 3t – cos(nt), evaluate at t =;

A: Given that x=t+2sinπt, y=3t-cosπt, we have to find dydx at t=12. Now, dydx=dydtdxdt…

Q: _4. Arg (zz) = 0, whenever :+0. _5. Arg(=)= arctan 2| for x +0, wherex= Re(z) and y = Im (z). 6. Arg…

A: This is a problem of complex analysis.

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

A: Given:           ∫01sin(lnx)ln(x)dx          Let ∫01sin(lnx)ln(x)dx=I…

Q: 3. Use the theorem in Sec. 48 to show that (z – zo)"- dz = 0 (n = ±1, ±2, ...) when Co is any closed…

A: The given question is solved below.

Q: 1. Prove that the composite trapezoidal rule with h = 2-i, i E N, is exact for ſ cos? (Tx) dr

A: We know that in composite trapezoidal rule, we approximate the integral as follows: ∫abf(x) dx ≈  h…

Q: Use symmetry to evaluate the followingintegrals.

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Q: 11. An expression that is equivalent to 2tan z Otan z Ocot z 02 cot z sin 2x 1-cos 2z is

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Q: -tan(z) %3D z*+cos(z) dx Select one: O a. None 5sin(z) Ob. ²+coz² (z) Oc. O d. 0

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Q: fhe coefpicient an fiderivative what? rin (2x ) in the fre of of F (A CoS is ン

A: We have to find the coefficient of sin 2x for given problem.

Q: Led xe R be such thad Xn→x, show that %3D

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Q: 5. Demonstrate the following identity: Ecosnt : cosme sin (m+1)0 sin n=0

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Q: If I, = e cos" zdr, where n > 2, Prove that i) I, =1-n e sin z cos"- rdr

A: Given,  In=∫0π2e-xcosnxdx solving by using Integration by parts, Formula of integration by parts,…

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

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Q: let Po)- tar'c) + tant (L). show that Plx)=C,where cis a constant and then Aind C

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Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: Evaluate: / sech[in cosr Janx dx A -2 tan-1(e cosx) +c cOsx B) None 2 tan -(e cOx) + C COSA D - 2…

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Q: Use symmetry to evaluate the followingintegrals.

A: The given integral is ∫-π4π4sec2xdx

Q: Fird the Aren of the Reyion c2-9 cos In teriur of (2€)

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Q: Let 1973 - sinh(1/(2z)) and : (0, 27]→C, Then, (t) = 3 cos(t) - 13 sin(t) %3D 2Ep1070 1971 |F(z)dz =…

A: We have to evaluate the complex integral ∫γfzdz, where the complex function fz=1z-2+sinh12z. First,…

Q: Find the edlution of the following equstions: (osx<r) a) cosx- casx =0 . b) tan2x = 3 tan X Sin8X .…

A: We have to solve the following equations.

Q: Choose true or false of the following 1- S, x? = 1 2 %3D 3 2- J sin x dx = 2 3- Se* X² dx = xeX + c…

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Q: 학과 학번 Determine the value(s) of d satisfying that Lacos(br+c) + d de lim 2-0c tan r dr for any real…

A: Integrate as follows.

Q: D. Use the Wronskian to detcrminc whether or not the vcctors arc independent or not (the answer for…

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Q: Let w = x*y cos s(4z). Find the following.

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Q: tan? z sec? x + sec a Prove 1-cos I

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Q: Select the definitions of sinhx, tanh a, and sech z. O e +e- e -e-z O e-e e +e-z O e -e e +e- O e +e…

A: The hyperbolic function of sine is expressed as-     sinh x=ex-e-x2 Thus, Option (C) is the correct…

Q: which of the foliowing is a vaiid equ be us ed to Soiue for 2 ak di altan 40=x 60 60 bl Sin 4O= 40…

A: Given : A right triangle

Q: T/2 COS z xp V4 - sin? a

A: givenI=∫0π2cosx4-sin2xdxsubstitute  sinx=t therefore limits will change t=sinπ2=1  to t=sin0=0after…

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: Let F = 2y ln zi+2x ln zj+2² k. Which of the following(s) is/are applicable to solve F· dr Sc is the…

A: The ways to solve given integral are

Q: In the case when U = x on the edge y = a (where Yo is a constant), a calculate C, inorder to show…

A: Given at y=a, U=ψ0ax     …Equation(1). And, on substitution of y=a in expression…

Q: S-) Find the gereral solufon of Sin'x y"- (2sinx.cos x)g'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Given differential equation is sin2xy"-2sinxcosxy'+cos2x+1y=sin3x Here, qx=sin3x Given that y1=sinx…

Q: lim, ,0* Sõ sin(t*) =? O a. 00 O b. 1/3 O.c0 O d. 2/3 O e. Limit does not exist е.

A: The correct option is, option (b), i.e. 1/3 The detailed solution is as follows below:

Q: A. Ifw= sin(x+bt)+cos(2x+ 2bt) . Prove that ôx? B. If f = x*y* + 2y sinx + x² lny then show that fxy…

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Q: (a) If u(x, y) = cos-1*" + y* ) x² + y? = COS then prove that ди du + y = -2cotu

A: Given: ux,y=cos-1x4+y4x2+y2

Q: - Show that u(x,t) e-a't[A sin(2x) + B cos(Ax)] satisfies the PDE uz = a?uxx for arbitrary A, B and…

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Q: Evaluate: / (In(2r – 1) – () + 25) da + 25 ) dx | Limits: [1, 6] Using Trapezoidal, n = 30

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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: 1 And the radios of Co for the pover Serie for the Power Serie vergence 00 xh (2"+1) (n?+1)

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Q: Prove the following idenbter P Sin (D + Sin(T a Cos A a 4

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

Q: Integrate the following (a) / tan(z)dx (b) Ju 1 dr /ez – 1 In 2

A: Evaluate the Integrals: (a) ∫tan x dx=∫sin xcos x dx Let cos x =t implies -sin x dx =dt , substitute…

Q: Verify the rule by differentiating ∫ du/(a2 + u2) = (1/a) arctan (u/a) + C . Let a &gt; 0.

A: Consider the given integral identity. ∫dua2+u2=1aarctanua+C Differentiate the LHS of the equation…

Q: (a) Evaluate O ezz C cos(TZ) where c is z = 1

A: The objective is to evaluate ∮Cez2cosπz where C is z=1 Singularity of ez2cosπz are,…

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

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Q: Write proofs in two-column form.

A: Given: QR and ST bisects each other.   Proofs: