2 cos Ø sinotos"0 csc0 Reuorite the expresson as a single triganometrie function whose anqument is 2O.

Q: az Let z=xy-e'siny, x-uv, y=7Vu?+v?. Then at (u,v)=(7T,0) is du

A: Given that z=xy-exsiny, x=uv, y=7u2+v2find ∂z∂u at u,v=7π,0

Q: A membranc of uniform density area is stracthed on a Circular frame of radius A to uniform stress…

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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: Let F = Vowhere o = e cos (Vy ). If C is the cardioid defined by ((2+ sin 0) sin 0, (2 + sin 0) cos…

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Q: Fend the area of the regian that bes de the fest curve and de the second curve. 13cose cos

A: Given that, Two polar curves  We have to find the area of the shaded region. First, find the…

Q: find area Inside the oval limaçon r = 4 + 2 cos 0 Inside the cardioid r Inside one leaf of the…

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Q: Q find Soluti on Of ion or me Vibrating equati Violin Shing azucxit) 6² Q?U (xit 1) 2. 2. which has…

A: Given an initial value problem, ∂2ux,t∂t2=c2∂2ux,t∂x2 With boundary conditions, u0,t=0 and uL,t=0.…

Q: Find the area Inside the cardioid r=2 cos (6/3) and outside the circle of radius r = vZ centered at…

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Q: +tlnt +tInt If x=sin and Jy= = cos prove that y"=c constant +eco te'

A: Given: x=sint2+tlntt4+etcost and y=cost2+tlntt4+etcost

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

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Q: The coefficient of sin(x) in the antiderivative of Flx)=(cos() is 15/32 (use fraction form not…

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

A: Convergence of the sequence

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

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Q: а. х %3 (3, —4,0, у b. х %3D (2, 1, —3, 4y c. x = (sen k, cos k, 24y para un entero positivo fijok

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Q: 9x cos(y) dA, D is bounded by y = 0, y = x2, x = 1

A: This is a problem of multi-variable calculus.

Q: af ar fe Consider f(1, y, z) = r² + y²z² and I=r sin 0, y =r cos 0, z = Or³. Find and

A: The function fx,y,z=x2+y2z2 and the polar transformation coordinates are x=rsinθ, x=rcosθ and z=θr3.…

Q: d Jcose d cose 'cos(r sin 0)]= [e* Telcom sin(tsin 0)]. (i) Show that t. %3D dt

A: (b) (i) show that t·ddtet cosθ cost sinθ=ddθet cosθ sint sinθ consider left hand side  t·ddtet cosθ…

Q: (b) f(u) = tan(arccos u). FRAS SER UNIVE ERS %3D ERSI TY OF fficial que s test question question ion

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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: Let y = cosh(ina²) then find y'. sinh (2n Ina) a. O b. O c. - sính(ina"). 2 O d. – sénh(2a. Ina²) O…

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Q: a. Show that If z=x+ iy where y 1 b. Evaluate: cosh (iz) + sin (2)

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Q: The coefficient of sin(2x) t F(x) =(cos() is Blank 1 (use fraction form not decimal no space) in the…

A: To determine the coefficient of sin2x in the antiderivative of Fx=cosx26.

Q: which u-sub will help integrate this? A. u = dx 11 [arctan(x)]" dæ = [9 + 12 cos(x)]" B. u 9+ 9x2 C.…

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Q: Is it true that Arg(z) = arctan for x + 0, where x = Re(z) and y = Im (z) ?

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Q: The antiderivative of Cos(3x) is Blank 1 (use small letter no space)

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Q: Find the area which is outside the curve r 4 cos 20 but inside the curve %3D r = 2.(

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Q: Under what conditions for the contants a,b, k,e =) is (aa+by) da + (ka + ly) dy = 0 exact? Solve the…

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Q: Use the convolution theorem to show that cos T sin (t – T) dr 1 sin t. %3D 2

A: Convolution theorem use integration of product of 2 functions and transforms them to pointwise…

Q: Find the diih of y integral tanar 230 e dn dy a) | shso b) c) O sysl-z 1-2 d) Nove of theoe

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Q: EXpress ume trig fatIOS as TTACCTIOTIS TII Smmpiest teTIIS. 16 R. V33 17 sin R = Cos S sin R and cos…

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Q: H.W. using the relation r = VT show that/(x) = COS X %3D 2

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Q: Verify if zo = 0 is a removable singularity for sinh z (ii) sin z3 (i) z2 (ii) 2³e/=, Explanations…

A: A limit is a mathematical object perceived to represent the last object in a sequence of the same…

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

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Q: What is the area of one of the petals of the rose curve r = 2 cos(20)? T/4 cos (20) d0 8. cos (20)…

A: We have to find

Q: 26. Inside the lemniscate r² = 6 cos 20 and outside the circle r = v3 V3 %3D

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Q: Use Green’s Theorem to evaluate ∮C squre toot of (1 + x^2)dx + 14x dy, where C is the triangle from…

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

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

Q: f : [o,s] → A? flt) = ( 6E) 2 cosh 3t, - 2 sin 3t, Compute f'lt).

A: If f(t) is differentiated with respect to t, then f'(t) is obtained. Let f(t)=x(t), y(t), z(t), then…

Q: What is the area within the curve r = cos 5θ?

A: For the solution follow the next step.

Q: fe and dr af Consider f(x, Y, z) = x² + y²z² and r = rsin 0, y = r cos 0, z = Or³. Find

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

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

Q: U + zu, =z u(z,0) = sin(87z) cos(90r). IER, t> 0,

A: Solving given partial differential equation by Lagrange method. Rewriting partial differential…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.