Sara
I’m having trouble with one of the WebWork problems. I’m given the function
f(x,y) = \sqrt{\tan(x)+y}
and the unit vector \left<-3,2\right>. I’m asked to find
a) \nabla f(x,y),
b) \nabla f(-0.2,7), and
c) D_{\vec{u}} f(-0.2,7), where \vec{u} is a unit vector pointing in the direction of the given vector \left<-3,2\right>.
I’ve got the first two just fine:
For part (a), I entered:
< 1/2 (tan(x)+y)^(-(1/2))sec^2(x), 1/2 (tan(x)+y)^(-(1/2))(1)>
and for part (b), I just plugged in the indicated values of x and y to get
<0.1995,0.1918>
Part (c) is pretty much the same. I first need to find the unit vector \vec{u} by dividing the given vector by its length, which is \sqrt{13}. I ended up getting
\vec{u} = \left<-\frac{3}{\sqrt{13}}, \frac{2}{\sqrt{13}}\right>.
Plugging that in, I got:
-(3/(13)^( 1/2 ))(0.1995)+ 2/(13)^( 1/2 ) (0.1918)
which is about -0.0596025. That’s marked incorrect, though. Any thoughts about where I might have gone wrong?