Find the length of L of the Curuc R Ct) = e2* cos (E) î +e?* sin (t) ĵ +ea* 1tsin (t) ĵ teat Ŕ over Hhe interual [,4.

Q: Evaluate the iterated ntegral by Lonverting to polor coordinates. 2. zy dx dy 34

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Q: If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). -…

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Q: Evaluate the iterated integral: a S " cos(2) dy dar.

A: Given that the double integral

Q: Find r' (t) where r(t) = (t sin t, t cos t, e"). O (cos t, – sin t, e2t) O (t cos t + sin t, sin t –…

A: We have to find derivative of the function: rt=tsint,tcost,e2t We know following rule for…

Q: use the definition prove that s d sinZ %3D Tal

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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.

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A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: Find the exact length of the cur x =t sin t y =t cos t for 0 <t < 1.

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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 Cauchy integral formulas to evaluate the eiz COS Z -dz, 2²(2z – 37)* where C is the region…

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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: If h(z) = sin (z) + sin(z°), find h'(z). a. 6s in (z)cos(z) +6z°cos(z°) Ob.6cos (z)sin(z) +…

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Q: Find the area enclosed by the loop of the strophoid r = 2 cos 0 – sec 0 -

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Q: šiven r,(t)=sin5ti +cos 5tj+\t+2k and r,(t)=5ti+2k , calculate "[r, (0) •r, (0)]. dt

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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: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

Q: التاريخ اليوم موضوع الدرس A) Discuss the conrergence of facx) %3D on A = Co,0)

A: Convergence of the sequence

Q: Find the sum of the residues of f (z) = sin z at its poles inside the circle |z| = 2. z cos z

A: Residue theorem∮f(z)dz=2πi(R1+R2+.........Rn)             =2πi(sum of the residues at the poles…

Q: Evaluate the integral S CO|CT CT | CO CT /Co NIC 8 dx using the two-point Gaussian quadrature rule.…

A: We have to evaluate the integral ∫−22816+x4dx using the two-point Gaussian quadrature rule. Here,…

Q: Evaluate the integral. |a cos(6 z) dz =| %3D

A: Topic:- integration

Q: Sinex dx is a) Conv. to o 6) diverge b) cont. to 프 auou (P

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

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Q: Show that the function e cosy ti Siny) is an andlytic Runction 2 W= Sin Z Q2. Determine whe ther…

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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: (a) Evaluate where c is z = 1 %3D c cos(Tz)

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Q: Show that the area of the surface of the solid generated by revolving the cardie r = a(1- cos 0)…

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

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Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dĩ (6) where C is the…

A: (6) Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

Q: 3. Evaluate the integral cosh ™z dz, z(z? + 1) Izl=2 where the circle |z| = 2 is described in the…

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Q: 2. %3D be Centered in a batt co,ogo) andradies I 2. frove thet S-273R

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Q: Evaluate the integral. cos(6 z) dz %3D

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Q: dy is then da In a If y = cosh r

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Q: Evaluate the integral cosx dx from T/3 to Tu2 O 0.293 О 0.134 O 0.500 O 0.707

A: To evaluate the definite integral we didn't consider the integral constant at the end of the result.…

Q: 10 Compute r''(t) when r(t) = (tº,3t, cos r'(t) = %3D

A: The differentiation is a process of finding the rate of change of one variable with respect to…

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: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian.

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

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Q: determine the area inside of the inner loop of the limaçon r = 2 cos 0 – 1.

A: We have to find area of r= 2cos(theta)-1

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

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