Use the divergence of the vector field to compute F(x, y) У · (tan-¹ (2x))i + (xy − 2 + 8x²) j - = 4 tan fo where C is the cardiod r = 1 + sin 0. (2x) 4 У dy - (xy − 2 + 87²) dx, -

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A: Solution :Given :    ∀4≤n∈ℕTo Prove :  2n &lt; n!

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Q: A spherical vector field is given by F(r,0,0)=2r cos(0) êr + 3r sin(0) ê +0(π- 0) ê. i) Compute the…

A: It is given that Fr,θ,ϕ=2rcosθe^r+3rsinθe^θ+θπ-θe^ϕ. Thus, F1=2rcosθ, F2=3rsinθ, and F3=θπ-θ.