For the given position vectors rt compute the tangent veloci

For the given position vectors r(t), compute the (tangent) velocity vector r\'(t) for the given value of t. A) Let r(t) = (cos 4t, sin 4t). Then = ( , )? B) Let r(t) = (t2, t3). Then r\'(2)=( , )? C) Let r(t) = e4t i + e-2t j + tk. Then r\'(5) = i + j + k?

Solution

A). r\'(t)=(-4sin4t,4cos4t) thus (0,4)................................B).r\'(t)=(2t,3t) thus (4,6)..............................C)r\'(t)=4(e)^4t i - 2(e)^-2t j + k thus (4(e)^20)i +(-2(e)^10)j + k)