31.
32.
38.
Part B
(B) Since the equation of the spiral is r = ln θ, use the polar mode. The
formula for area in polar coordinates is
Therefore, calculate
The result is 3.743.
(C) When y = 2t = 4, we have t = 2, so the line passes through point F(2)
= (5,4).
Also so at t = 2 the slope of the tangent line is
An equation for the tangent line is y − 4 = ln 2(x − 5).
(C) The limit by substitution is of the form
so apply
L’Hôpital’s Rule. You get which is still of the form
therefore apply
L’Hôpital’s Rule again. The new limit is by substitution is
