r(x)=(e^xsin(x), e^x, e^xcos(x))
find the parametric equations for the tangent line at x=0 and pi/2
can someone help me with this
Did you state the equation exactly as it was given? This written in an unusual way. Usually the nation for an equation like this is:
$\displaystyle r(t)=< e^{tsin(t)},e^t,e^{tcos(t)} >$
where t is the parameter. The parametric equations for the curve are:
$\displaystyle x =e^{tsin(t)}$
$\displaystyle y=e^t$
$\displaystyle z =e^{tcos(t)}$
So I take it that you are trying to find the equation of the tangent line corresponding to the parameters t=0, and then the tangent at $\displaystyle t=\frac{\pi}{2}$ correct?
The components of the derivative of a vector function are the derviatives of the components.
$\displaystyle r'(t)=< \frac{dx}{dt},\frac{dy}{dt},\frac{dz}{dt} >$
Now just plug in the given parameters.