Attached is a document showing my steps in finding the curvature of a curve for a vector valued function. I'm sorry I didn't type it out here - it is simply too much for me to do. The problem was:
Find the curvature of the curve [MATH]r(t)=<4\cos(2t),3\sin(2t)>[/MATH] at the points [MATH]t=0 \text{and} t=\frac{\pi}{4}[/MATH]. My work is on the attached document. I feel confident about my answer for t=0 but not for my answer with [MATH]t=\frac{\pi}{4}[/MATH] (that one did not match up with an answer key. Any insight?
Find the curvature of the curve [MATH]r(t)=<4\cos(2t),3\sin(2t)>[/MATH] at the points [MATH]t=0 \text{and} t=\frac{\pi}{4}[/MATH]. My work is on the attached document. I feel confident about my answer for t=0 but not for my answer with [MATH]t=\frac{\pi}{4}[/MATH] (that one did not match up with an answer key. Any insight?