The Bernoulli spiral, shown below, is parametrized by r(t) = et cos(4t), et sin(

Question

The Bernoulli spiral, shown below, is parametrized by r(t) = et cos(4t), et sin(4t) Show that the spiral has the property that the angle between the position vector and the tangent vector, , is constant. Give an approximate value for in degrees. A bug crawls along the spiral, according to the pararametrization r(t), starting at the beginning of time, t = - We can't plug in because it is not a number, but we can take a limit. What is the bug's starting position, at the beginning of time? Find the speed of the bug as a function of time, and the distance travelled up to an arbitrary time T. Is r(t) an arc-length parametrization? Explain. When a curve in the plane is the graph of a function y = f(x), it can be easily parametrized

Explanation / Answer

yes, r(t) is an arc length of parametrization.

because

t is angle here , means this is a polar curve with theta =t.

and in polar curve we know that ,

r(theta) is arc length of the curve.

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