Find the parametric equations of the line that is tangent to the curve of intersection of the surfaces $x=z^2$ and $y=z^3$ at (1,1,1).

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Illustrate by graphing both the curve and the tangent line on a common screen. x = t cos t, y = t, z = t sin t; (-π, π, 0)

Find parametric equations for the tangent line to the curve with the given parametric equations $x = t, y = e^{-t}, z = 2t - t^2$ at the specified point (0, 1, 0). Illustrate by graphing both the curve and the tangent line on a common screen.

Find the points on the curve with parametric equations $x=t^3-t$ and $y=t^2$ at which the tangent line is parallel to the line with parametric equations $x=2t$ and $y=2t+4$.

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Illustrate by graphing both the curve and the tangent line on a common screen. \

$$x=t, y=\sqrt{2} \cos t, z=\sqrt{2} \sin t ; \quad(\pi / 4,1,1)$$

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

$$x=e^t, y = te^t, z=te^t2; (1, 0, 0)$$

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Illustrate by graphing both the curve and the tangent line on a common screen.

$$x = 2 cos t, y = 2 sin t, z = 4 cos 2t; (√3, 1, 2)$$

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. $x=\ln t, y=2 \sqrt{t}, z=t^{2} ; (0,2,1)$

Find parametric equations for the tangent line to the curve with the given parametric equations $x = 2\cos t, y = 2\sin t, z = 4 \cos 2t$ at the specified point $(\sqrt{3}, 1, 2)$. Illustrate by graphing both the curve and the tangent line on a common screen.

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

$$x=t^5, y=t^4, z=t^3 ; \quad(1,1,1)$$

Find the unit tangent vector T(t) at the given point on the curve.

$$\mathbf{r}(t)=\left\langle t^3+1,3 t-5,4 / t\right\rangle, \quad(2,-2,4)$$

Find an equation of the tangent plane to the surface at the given point. f(x, y) = y/x (1, 2, 2)

Find a vector function that represents the curve of intersection of the two surfaces. z=(x^2+y^2)^1/2 and the plane z=1+y

Find a vector equation and parametric equations for the line segment that joins P to Q.

$$P(-2,1,0), Q(5,2,-3)$$