Q2. In the circle Izl = 1, Find the upper bound for 1924+327+2

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Q: Find the area of one loop of the rose defined by the equation r=cos2θ.

A: Given

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A: Use the formula for the arc length then standard integral then simplify the result.

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A: Please refer the attached image for complete solution.

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A: Second option is correct answer i . e . I = -1-cosh(π)+π(i-1)

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A: Arc length is given by s=r.θwhere r = radius of the circle and  θ = central angle in radian

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Q: 2 X- - SS. T dydx

A: ∫1-1∫0x2-1dy dxWe need to evaluate the above double integral.

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A: differentiate y with respect to x .

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A: topic-displacement

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A: (11) Consider the provided question,

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A:

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A:

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Q: Use the Trapezoid Rule withn 5 to approximate e dr. 074035 2.9614 O37.0175 O 1.4807

A: The trapezoidal states that

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A: Given:  It is required to find the area right to z= 2.54.

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A:

Q: Let C be the shortest path that connects à to ni and I = S. (sinhz +1)dz. Then

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A: The methods to solve the given integration are

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Q: 12) Find the exact length of the curve [4,16] on 3

A: We can find the exact length of the curve as below,

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Q: 7 74 12. eint) Prove that (-",) lies on the unit circle. 6.

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A: By using equation of circle formula, we find the required equation of circle.

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Q: 2.2 Find upper bound of zp (z- 3i)3 + 1 where C is the circle |z - 3i = 4. 2.3 Use the Cauchy…

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Q: Let C be the shortest path that connects n to ni and I = S. (sinhz + 1)dz. Then O I=-sinh n+ Ti(i-1)…

A: Option C true.

Q: r = √3 − 2cos θ.

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Q: determine the area of one leaf(petal) of the rosde curve r = 2sin(3Θ)

A:

Q: A circle, with area A = Tr2, is expanding with time. dr If = 6 cm 2/s, what is dt dA when r= 2? dt…

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