Sketch the exponential spiral r= ae^(b*theta) for the case in which (a) is positive and b is negative, and ...

Question

show that the arc length from theta=0 to theta = ~ is equal to the length of the part of the tangent at theta=0. That is cut off by the x-axis and y-axis

u dont have to sketch it here. bcoz u cant

I just need explanation. what this is ??
w./ the a and b variable
and solve the length..

Answer 1

mat semua!

Answer 2

If a is positive the spiral goes clockwise as you move out. If negative, it's anticlockwise. In both cases, it gets looser and looser as you move out. So it looks like the spring on the escapement of an old-style clock.