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Moderate

# Find the Function of a Curve

MVCALC-XKERPR

Let $C$ be the curve defined by:

$$x^2+y^2=36$$

Which of the following vector-valued functions represents $C$?

A

${\bf f}(t)= t {\bf i} -\sqrt{36-t^2} {\bf j}$ with $0\leq t\leq 6.$

B

${\bf f}(t)= t {\bf i} +\sqrt{36-t^2} {\bf j}$ with $0\leq t\leq 6.$

C

${\bf f}(t)=6\cos t {\bf i} +6\sin t {\bf j}$ with $\leq t\leq 2\pi .$

D

${\bf f}(t)= t {\bf i} +\sqrt{36-t^2} {\bf j}$ with $-6\leq t\leq 6.$

E

${\bf f}(t)= -t {\bf i} +\sqrt{36-t^2} {\bf j}$ with $-6\leq t\leq 6.$