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cestrela7 [59]
3 years ago
14

determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give a counterexamp

le. The functions r1(t) = 3cos(t)i + 3 sin(t)j + (3cos(t) + 3sin(t)) k and r2(t) = ti, (9-t^2)j, t+(9-t^2) are different parametrizations of the same curve
Mathematics
1 answer:
Andrews [41]3 years ago
8 0

Answer:

FALSE

Step-by-step explanation:

No, they are not

<u>Counter-example: </u>

Take t = 4  

If r1 and r2 were the same curve, there should exist some value \bf\large t^* for which

\bf\large 4=3cos(t^*)

Taking the absolute value on both sides

\bf\large | 4 |=|3cos(t^*)|\Rightarrow 4=3|cos(t^*)|\leq 3

since the function cos(x) takes values between -1 and 1.

But 4 is greater than 3, and we have a contradiction.

So, r1 and r2 are not the same curve.

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