Math 115H (Assignments)

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1. For what value(s) of $t$ is $\left<3t-t^3,2t^2\right>$ a vertical vector?

2. For what value(s) of $t$ is $\left<1-\cos t,{\sqrt3\over 2}+\sin t\right>$ the longest? What is the greatest length, and what vector(s) achieve it?

   [Hint: It might make it easier to note that since the length is never negative, it will be longest when its square is longest. Note also that since the length is a number that depends on $t$, it is a single-variable function, so you can use single-variable calculus to determine the greatest length. Finally, don't forget that $\tan(t)={\sin(t)\over\cos(t)}$.]

Math 115H (Fall 2013) web pages Created: 9 Oct 2013 Last modified: Oct 9, 2013 2:29:07 PM Comments to: dpvc@union.edu

Assignments