Evaluate (if possible) the vector-valued

Question

function at the indicated value of t.
r(t) = rt{t}i + [t^(3/2)]j + [e^(-t/4)]k
at t = [9 + delta(t)]

show me step plllllz

Answer 1

I wish I knew what
rt{t}
meant but anyway

we will need to do r of 9 and delta r for delta t at t = 9

r = t i + t^1.5 j + e^.25 t k

dr/dt= i + 1.5 t^.5 j + .5 e^.25 t
so
dr (your delta r)
= dt i + 1.5 t^.5 dt + .25 e^.25 t dt j

Then
r(9)= 9 i + 27 j+ 9.49 k
dr = dt i + 4.5 dt j + 4.5 dt j

now add :)
(9+dt) i + (27+4.5 dt)j + (9.49+4.5 dt) k