Question

Find r'(t) and r''(t) for the given vector function f(t)= lnti+j, t>o

Answer 1

Answer:

xample 2.4.1

Let

r(t)=ti^+etj^−3t2k^.

Find T(t) and T(0) .

Solution

We have

v(t)=r′(t)=i^+etj^−6tk^

and

||v(t)||=1+e2t+36t2−−−−−−−−−−−√.

To find the unit tangent vector, we just divide

T(t)=v(t)||V(T)||=i^+etj^−6tk^1+e2t+36t2−−−−−−−−−−−√.

To find T(0) plug in 0 to get

T(0)=i^+e0j^−6(0)k^1+e2(0)+36(0)2−−−−−−−−−−−−−−√=i^+j^2–√=12–√i^+12–√j^.

Step-by-step explanation:

tq