- 113

- 0

**1. Homework Statement**

Let bar r(t) = < -1t^(2)+2, -3e^(5t), -5sin(-4t) >

Find the unit tangent vector `bar T(t)` at the point `t=0`

**3. The Attempt at a Solution**

Attempt:

r(t) = -1t^2 + 2, -3e^5t, -5sin(-4t)

v(t) = -2t, -3e^5t, -5cos(-4t)*-4

T(t) = (-2t - 3e^(5t) - 5cos(-4t)*-4)/sqrt(-2t^2 - (3e(5t))^2 - (5cos(-4t)*-4)^2)

=

(0 - 4 + 20)/sqrt(0 - 9 - 400)

T(0) = <0, -4/3, 20/20.2237>

Actual Solution:

`bar T(t) = < 0,-0.6,0.8 >`

Sorry about all these questions but these unit tangent vectors have got me stumped...