(a) Find the arc length function for the curve measured from the point in the…

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

(a) Find the arc length function for the curve measured from the point

P

in the direction of increasing

t

and then reparametrize the curve with respect to arc length starting from

P

. (b) Find the point 4 units along the curve (in the direction of increasing

t

) from

P

\mathbf{r}(t) = e^t \sin t \mathbf{i} + e^t \cos t \mathbf{j} + \sqrt{2} e^t \mathbf{k}, \quad P(0, 1, \sqrt{2})