Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find
the flux of F across S, the part of the paraboloid x2 + y2 + z = 29
that lies above the plane z = 4 and is oriented upward.
a) Evaluate the limit lim x→0 tan(2x) / x
b) Differentiate y = x^tan(x)
c) Find the equation of the tangent line to 4x^2 + 2xy−y^2 = 4
at the point (1, 2).
d) Differentiate f(x) = arctan(x^2 + 1)
e) Differentiate f(x) = ln(cosh x)
Thank you!
a. tan ^ -1(y/x) Show that the function u(x,y)define classical
solution to the 2-dimentional Laplace equation Uxx+Uyy =0
b. e ^ -(x-2t)^2 Show that the function u(t,x) is
a solution to wave equation
Let f ( x , y ) = x^ 2 + y ^3 + sin ( x ^2 + y ^3 ). Determine
the line integral of f ( x , y ) with respect to arc length over
the unit circle centered at the origin (0, 0).