Finding a Limit Using Polar Coordinates In Exercises 57-60, use polar coordinates and L'H6pitals Rule to find the limit.
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Multivariable Calculus
- Channel flow The flow in a long shallow channel is modeled by the velocity field F = ⟨0, 1 - x2⟩, where R = {(x, y): | x | ≤ 1 and | y | < 5}.a. Sketch R and several streamlines of F.b. Evaluate the curl of F on the lines x = 0, x = 1/4, x = 1/2, and x = 1.c. Compute the circulation on the boundary of the region R.d. How do you explain the fact that the curl of F is nonzero atpoints of R, but the circulation is zero?arrow_forward(a): Present the correct definition for Rotational, Divergent and Laplacian. (b): Introduce the Jacobian and the Jacobian of some function. (c): Present the correct definition of Double Integral.arrow_forwardPseudometric spacesarrow_forward
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- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning