Sketch the parametric curve for the following set of parametric equations. Clearly indicate direction of motion 1)x=5cost 2)y=2sint 3)0>=t>=2pi

Use the given graph off over the interval (0, 6) to find the following.

a) The open intervals on whichfis increasing. (Enter your answer using interval notation.)
b) The open intervals on whichfis decreasing. (Enter your answer using interval notation.)
c) The open intervals on whichfis concave upward. (Enter your answer using interval notation.)
d) The open intervals on whichfis concave downward. (Enter your answer using interval notation.)
e) The coordinates of the point of inflection. $(x,y)=$

For the given rectangular equation, write an equivalent polar equation. $x^2+y^2-10x=0$

Replace the Cartesian equation with equivalent polar equations. xy = 2

State the Fundamental Theorem for Line Integrals

Find all points (if any) of horizontal and vertical tangency to the curve:
${\displaystyle x=1-t.y=t^2}$

Find a vector equation and parametric equations for the line segment that joins P to Q . P(2, 0, 0), Q(6, 2, -2)

Compute the derivative of the vector-valued function ${\displaystyle r\left(t\right)=⟨\sin 2t,e{t}^2⟩.}$