x - Balliol College - University of Oxford
x - Balliol College - University of Oxford
x - Balliol College - University of Oxford
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SJ Roberts - July 2011 Revision 1/ page 10<br />
40. What is the angle between the vectors i 2j<br />
3k<br />
and 3 i 2j<br />
k <br />
41. Find the vector position <strong>of</strong> a point 1/3 <strong>of</strong> the way along the line<br />
between x , y z and x , y z , and nearer x , y z .<br />
1 1,<br />
1<br />
2 2,<br />
2<br />
1 1,<br />
1<br />
42*. At time 0<br />
t two forces f1 i<br />
j<br />
and f1 2i<br />
2j<br />
start acting on a<br />
point body <strong>of</strong> unit mass lying stationary at point (1, 2) <strong>of</strong> the x,y<br />
plane. Describe the trajectory r(t) <strong>of</strong> the particle.<br />
Some answers and hints<br />
1. 10 x<br />
2. 4 sec x<br />
3.<br />
2<br />
x<br />
4 e<br />
4.<br />
2<br />
1<br />
1 x<br />
2<br />
5. 12x<br />
sinx<br />
<br />
6.<br />
12x<br />
3<br />
e<br />
3x<br />
4<br />
2<br />
7. x cos x 2x<br />
sin x 8.<br />
x sec<br />
2<br />
x tan x<br />
2<br />
10. minimum at (x, y) = (0, 0), maximum at 2,<br />
4e<br />
<br />
x<br />
2<br />
2 <br />
9. 80 400 / e 134. 1<br />
11.<br />
5 4<br />
5<br />
3 3 x x<br />
b a 12. C 4<br />
1 6<br />
13. cos x C<br />
6<br />
2<br />
14. x C<br />
1 15. 16. log cos<br />
xC<br />
e<br />
1<br />
x <br />
17. sin x C 18. sin<br />
1<br />
C 19. x cos x sin x C<br />
a
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