Julia White
2021-12-20
Answered

If a curve has the property that the position vector $r\left(t\right)$ is always perpendicular to the tangent vector ${r}^{\prime}\left(t\right)$ , show that the curve lies on a sphere with center the origin.

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asked 2021-05-14

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.$(x,\text{}y)=$

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.

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Find parametric equations and symmetric equations for the line.

The line of intersection of the planes

$x+2y+3z=1$

and

$x-y+z=1$

The line of intersection of the planes

and

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Find the exact length of the polar curve.

$r={\theta}^{2},\text{}0\le \theta \le 2\pi$

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Consider the parametric equation

a)Eliminate the parameter to obtain an equation in x and y.

b)Sketch the graph of the equation

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Verify the Sum and Product Rules for derivatives of vector-valued functions.

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Represent the plane curve by a vector-valued function $y=9-{x}^{2}$