## Calculus 8th Edition

Given; $|r(t)|=1$ for all the value of $t$ $1$ can be written as; $Sin^{2}t+cos^{2}t=1$ Let us suppose our function as $r(t)=(Sin(t^{2}),cos(t^{2}),0)$ Then $r'(t)=(2tcost, -2t sint,0)$ $|r'(t)|=\sqrt{4t^{2}. cos^{2}t+4t^{2} sin^{2}t}$ $=2t(1)$ Thus, $|r'(t)|=2t$ which is not a constant. Hence, the given statement is false.