Find r'(t)·r''(t) of r(t) = <2e²t, 4e⁻²t, te²t>

[chickyroger]

Homework Statement

If r(t) = \left\langle\2e^{2t},4e^{-2t},te^{2t} \right\rangle, find r'(t) \cdot r''(t).

Homework Equations

r'(t) = \left\langle4e^{2t},-8e^{-2t},2te^{2t}+e^{2t} \right\rangle
r''(t) = \left\langle8e^{2t},16e^{2t},4te^{2t}+4e^{2t} \right\rangle

The Attempt at a Solution

r'(t) \cdot r''(t) = 32e^{2t} - 128 + 8t^2e^{2t} + 8te^{2t} + 4te^{2t} + 4e^{2t}
r'(t) \cdot r''(t) = 36e^{4t}+8t^2e^{2t}+12te^{2t}-128

I cannot see why my answer is wrong. Please help!

 

[vela]

Fixed your post to make it readable:

Homework Statement

If \mathbf{r}(t) = \langle 2e^{2t}, 4e^{-2t}, te^{2t} \rangle, find \mathbf{r}&#039;(t)\cdot\mathbf{r}&#039;&#039;(t).

Homework Equations

\mathbf{r}&#039;(t) = \langle 4e^{2t},-8e^{-2t},2te^{2t}+e^{2t} \rangle
\mathbf{r}&#039;&#039;(t) = \langle 8e^{2t},16e^{2t},4te^{2t}+4e^{2t} \rangle

The Attempt at a Solution

\mathbf{r}&#039;(t) \cdot \mathbf{r}&#039;&#039;(t) = 32e^{2t} - 128 + 8t^2e^{2t} + 8te^{2t} + 4te^{2t} + 4e^{2t}
\mathbf{r}&#039;(t) \cdot \mathbf{r}&#039;&#039;(t) = 36e^{4t}+8t^2e^{2t}+12te^{2t}-128

I cannot see why my answer is wrong. Please help!

You didn't combine the exponentials together correctly.

 

[HallsofIvy]

Homework Statement

If r(t) = \left\langle\2e^{2t},4e^{-2t},te^{2t} \right\rangle, find r'(t) \cdot r''(t).

Homework Equations

r'(t) = \left\langle4e^{2t},-8e^{-2t},2te^{2t}+e^{2t} \right\rangle

This is correct.
r''(t) = \left\langle8e^{2t},16e^{2t},4te^{2t}+4e^{2t} \right\rangle[/quote]
This is not but probably just a typo: the second component is 16e^{-2t}.

The Attempt at a Solution

r'(t) \cdot r''(t) = 32e^{2t} - 128 + 8t^2e^{2t} + 8te^{2t} + 4te^{2t} + 4e^{2t}

And you have propogated the typo: the product in the second term is (-8e^{-2t})(16e^{-2t})= -128e^{-2t}[/tex]<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <b>r&#039;</b>(t) \cdot <b>r&#039;&#039;</b>(t) = 36e^{4t}+8t^2e^{2t}+12te^{2t}-128<br /> <br /> I cannot see why my answer is wrong. Please help! </div> </div> </blockquote>