show that
To prove the gradient of the function \( \frac{r}{1 + r^2} \) in spherical coordinates, we can proceed as follows: Let the function be: \[ f(r) = \frac{r}{1 + r^2} \] The _________ ________ ___ ______ ________ ______ ___ _____ _____.
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a) Obtain the derivative and the unit tangent vector for a vector function
b) For a scalar field where n is a non-zero real constant, show that
Out of 90 applicants for a job, 60 people get selected after the interview. If five applicants are selected at random, calculate the probability that 2 will get selected.
a) Calculate the volume of the tetrahedron whose vertices are the points A = (3, 2, 1), B = (1, 2, 4), C = (4, 0, 3) and D = (1, 1, 7).
b) For three vectors
b) Determine the metric coefficients for the coordinate system (u,v,z) whose coordinates are related to the Cartesian coordinates by the following equations:
Is the system orthogonal?
show that
Using Stokes’ theorem evaluate where
and C is the circle
a) Determine the value of the constant a for which the vector field
is incompressible.
b) Show that for any vector field \bar