Old Final Exam Answers

1a. - 3     b. sqrt(5)     c. < 0, 2/sqrt(5), 1/sqrt(5) >   d. < - 6, 4, 2 >
 

2. r(t) = < 2 , 1, -3> + t<3, -3, 3>,  0 < t < 1

3. sqrt(34) 

Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(4*a, `<,>`(-5/13*sin(5*t), 5/13*cos(5*t), 12/13))*b, `<,>`(-cos(5*t), -sin(5*t), 0)) 

 

5. f(0, 2) = -16 local min.;  f(0, -2) = 16 saddle point;

6.  f(0, 2sqrt(2)) =  f(2sqrt(2), 0) = 16sqrt(2) is max,
          f(0, -2sqrt(2)) = f(-2sqrt(2), 0) = -16sqrt(2) is min.
 

14., 1.166666667*Pi, 1.166666667*Pi 

 

9a. f(x,y,z) = x^2 + xyz^2 + K    b. 324

 

11. e^2+7/15