Divergence and Curl In Exercises 19-26, find (a) the divergence of the
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- Consider the vector field. F(x, y, z) = (5ex sin(y), 5e sin(z), 8e? sin(x)) (a) Find the curl of the vector field. curl F = (b) Find the divergence of the vector field. div F =arrow_forwardSubject differential geometry Let X(u,v)=(vcosu,vsinu,u) be the coordinate patch of a surface of M. A) find a normal and tangent vector field of M on patch X B) q=(1,0,1) is the point on this patch?why? C) find the tangent plane of the TpM at the point p=(0,0,0) of Marrow_forwardGreen's Theorem as a Fundamental Theorem of Calculus Show that if the circulation form of Green's f(x)' Theorem is applied to the vector field ( 0,). where c > 0 and R = {(x, y): a SIS b,0 s ys c}, then the result is the Fundamental Theorem of Calculus, dx = f(b) – f(a).arrow_forward
- Sketch the vector field F = ⟨x, y⟩ .arrow_forwardProperties of div and curl Prove the following properties of thedivergence and curl. Assume F and G are differentiable vectorfields and c is a real number.a. ∇ ⋅ (F + G) = ∇ ⋅ F + ∇ ⋅ Gb. ∇ x (F + G) = (∇ x F) + (∇ x G)c. ∇ ⋅ (cF) = c(∇ ⋅ F)d. ∇ x (cF) = c(∇ ⋅ F)arrow_forwardSketch the vector field F(x, y) 1. 1 xi+ %3Darrow_forward
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