dz and Q\ let z = In (² + 1) where =r sine find dr OP

Q: aw 1(dw If w = f (x,y) and x=r.cos0, y=r.sine Prove that - * = $² + fy² ar 2a0

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Q: The appropriate trigonometric substitution for * dx is V3x-x 3 3 X ==+ sin 0 2 2 sec 0 4 2 O Option…

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Q: | cos r In(sin z)dr

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Q: Find the length of the astroid x = cos3 t, y = sin3 t, 0 ≤ t ≤ 2π.

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Q: (p² –1)cos[cosh (In r)]dr

A: In this question, we need to find the integral.

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

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Q: cos z dz (4 + sin z)?

A: The solution of above integral is written in below steps.

Q: 4 sin' t cos tdt 4 sin"(t) cos (t) %3D

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Q: 1₁ -1.2 - St 0 √x sin ex dx

A: Given :   I1=∫01.2xsinex3dx

Q: Find dy/dx for the following functi 5" + 5*y = In sin-1 e*

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Q: C. If w=f(x,y) and x = r. cose, y=r. sine. Prove that aw ar aw +1 (2001) = fx² + fy²

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Q: Find all x and y between O and 27 so that the equation is true. cosx+i siny = sinx+i x = 4 or 4y = 2…

A: Explanation of the answer is as follows

Q: sin(nz) b) E: on (0, 2x] n-1 AcoAnA

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Q: aw Q:3) Find ду if w 2u' v+ In(5v) , u=x+y & v=e"siny

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Q: S₁ + Sa cos²0 de 01/2000 sin ²0 de csc ³0 de + Sc 01/se sec ³0 de The integral dx (x²+4)² can be…

A: We have to solve above integral

Q: Eliminate the arbitrary constant/s of this equation to obtain the DE. Express the DE in general…

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Q: Check by differentiation that y = 2 cos t + 6 sin t is a solution to y"+y= 0 by finding the terms in…

A: Here,  y=2cost+6sint

Q: T/2 cos t dt 1 + sin²t

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Q: dz and Q\ let z = In (r² + 1) where r =r sin 0 find dr dz de

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Q: Determine the speed (in meters per second) of a particle with a trajectory (3 sin (3t), 8 cos (3t)),…

A: We have to find dsdtt0=π4

Q: Find Cuurtce at Pla,l, 이) (x 2y-1 Xe' î + X Cos (22), 3. (2²+)

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Q: (a) , f(r cos 0,r sin 0 )rdrde

A: Answer and explanation is given below

Q: ди If u = e* siny where x = st? and y = s²t. Find ди and at as

A: Given data: The given function is u=exsiny. The second expression is x=st2. The third expression is…

Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

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Q: dy There is no need to simplify. dr III. Find sin-'r + In 2 3coth z – tan(6r) 1. y = 20

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Q: - ual2) V17 – cos(27at) (2 – 4t) sin(#) Given f(r) = edt, find the equation of the line tangent to…

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Q: S Si dydx %3D 1-r

A: To evaluate the given double integral.

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: Calculate F-dr in the case when F(z,y) = (7y - sin (y) + 8)i+ (72 -e cos (y))jis conservative, and A…

A: Given that: F=7y−exsiny+8i+7x−excosyj and, rt=2tsinπt2i−π2sinπt2j for 0≤t≤1

Q: a. Show that If z = x+ iy where y 1 b. Evaluate: cosh?(-z) – sinh²(z)

A: Given that z =x+iy For a part , y<0 and we need to prove that | eiz | >1 For b part, we need…

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

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Q: dx 5) prove that sin x+c using method of trigonometric substitution. %3D

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Q: 2. Find sin(72) -dz. where C: z(t) = 2 cost+i (2 sint). Os ts 2m.

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Q: O sin (z)cos(z)dz

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Q: Inside the circle r =3 sin 0 and outside the cardioidr 1 + cos 0

A: The area that we have to calculate is the shaded area in the diagram above.

Q: Prove that L" (coshat sinat + sinhat cosat) %3D s*+4a*. 2a

A: The function F(s) is Factorize the denominator

Q: (a) Find dr dy given that x²y + sin xy = 0.

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

Q: dz Let z=sinh -(y-2x), where x = we and y=In then is given by du

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Q: 1. Use Green's Theorem to evaluate [(3ye* -7 sin (3x*))dx + (5x* +2x*y* +8e*-y* )dy, where C is the…

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Q: Fred show that Coshz-Coshx Cosy s +i Sinhx Siny O Coshiz= osz Sinh (iz)= j Sinz

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Q: I sin(z) cos(z) da : Hint:

A: Given integration is, ∫xsin(x)cos(x)dx We know that, 2sin(x)cos(x)=sin(2x) Now, the integration…

Q: The area between the two loops of the limacon r = 1+2 sin 0.

A: Question- The area between the two loops of the limacon          r = 1 + 2  sin theta .

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: /2 cos a sin(sin r) dx

A: using method of substitution

Q: +z/3 + sin z dz

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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: Sexyz ds, C: x= 2 sin t, y = t, z= -2 cos t, 0sts T

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Q: F- dr in the case when F(z,y) = (7y -sin (y) + 8) i+ (72 - cos (y))jis conservative, and Ais the…

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Q: dy If sinx + siny = xy, find dr coss-ly O a. -cosy cosx-y a-cosy none of these CORE-ty #coy CORE-Y…

A: The objective of the question is determine the derivative  and choose the correct option.