Register to reply 
Unit tangent vector to a curve at a point 
Share this thread: 
#1
Sep2309, 09:21 PM

P: 15

1. The problem statement, all variables and given/known data
Find the unit tangent vector T(t) to the curve r(t) at the point with the given value of the parameter, t. r(t)=<e^(2t), t^(2), 1/(3t)> t=1 2. Relevant equations none 3. The attempt at a solution So first I took the derevative to get r'(t) which I got to be <2*e^(2x), 2t^(3), 3t^(2)> and plugged in the paramter, 1, so I got <2(e^2), 2,3> and then I think I should divide that by its own magnitude, which I got to be the square root of (4(e^4) + 13) Buttt that's not working and Im not sure which part I went wrong on help? THANKS 


#2
Sep2309, 09:40 PM

Sci Advisor
HW Helper
Thanks
P: 25,228

The derivative of 1/(3t) is (1/3)*t^(2). Not 3t^(2).



#3
Sep2309, 09:43 PM

P: 15

Ohhh ok... can you kinda explain that? Isn't 1/(3t) basically (3t)^(1) and then you can use the power rule?



#4
Sep2309, 09:45 PM

P: 15

Unit tangent vector to a curve at a point
ohhhh i have to use quotient rule?!



#5
Sep2309, 09:47 PM

P: 15

ahhh yay i got it thanks!!! picking up calc againafter the summer sucks...



#6
Sep2309, 09:48 PM

Sci Advisor
HW Helper
Thanks
P: 25,228




#7
Sep2309, 09:49 PM

Emeritus
Sci Advisor
PF Gold
P: 4,500

Yes, but then you need to use the chain rule
[tex] \frac{d}{dt} (3t)^{1} = 1*(3t)^{2}*\frac{d}{dt}(3t) = 1*(3t)^{2}*3[/tex] 


Register to reply 
Related Discussions  
Unit Tangent For A Curve  Calculus & Beyond Homework  1  
Unit Tangent Vector at a Point  Calculus & Beyond Homework  6  
(Unit Tangent Vector)  Calculus & Beyond Homework  0  
Unit tangent vector in 3D  Calculus & Beyond Homework  7  
Unit tangent vector (cal 3)  Introductory Physics Homework  5 