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test2_sol_Winter_08

# test2_sol_Winter_08 - (b[6 Marks Find the tangential and...

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MATH 2008/09B Test 2 '\. February 12, 2{)08 NAME(PLEASE PRlNT): s.~~ STUDENT NO.: . Instructions: 1. This test has 4 questions and a total of 40 marks. 2. Calculators are NOT allowed. (Q1) [6 Marks] Find (u x v)' (1) if u(t) = (2t, lnt, cas (~t)) and vet) = (e1-t, yt, t3 + 1). u.. C.f) := C :2-1/ J"" -I: / ~ ( aJ)) -"-:> U ( I) =- (.); s G:; if) === (;). /{j/ (j ) [L it) ~( d; t ;- :! s.:. .( tJ:j)} -'"> () 1(1) - (d-; I;- gJ / / =:. U <. 1 J (\ AJ (\") -+- lA (\ ) ~ 1) (I ) == (.;1))_ gjx( \)\/).) -+ (;210)O)X(-\l~/3)

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(Q2) Let the plane curve C with equation y = x2 - x + 1 be given and the point P(l,l) lie on C; (a) [3 Marks] Find the curvature of C at the point P; . J f 1/(;0/ /L (?l):::- - 3/2- [I + Cf!(:iJ)z] I' 1/ f (?() ='1/:;; .?--.:t-!. .",.) (I).:: ;2-/::=1 t'l fit J ('1);:;;:;?~::> (I)::::' ).. (d) [2 Marks] [2 Marks] Write the equation of the Osculating circle to the curve C at the point P; 2 2 ( 1-) 2 2- _ ( r:x - 0') -+ ( ;- l);:: jc. . ~ (J;) := d-- ~ 2+ 1'3-2/= ~l
(Q3) A particle has the acceleration aCt) = (2, - t12' e1-t). Let V(1) ==(:J", \) -~ ') and 'f ( \").:::: (~J (j.;'\ '); (a) [4 Marks] Find the velocity and the position functions of the motion.

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Unformatted text preview: (b) [6 Marks] Find the tangential and normal components of acceleration vector at the point Q(l, 0,1); (b) [3 Marks] Find a scalar equation of the normal plane at the point Q(l,O,l). '""I"~ d.-0--r-d ~ ~-rD ;:::0 5,-,,-\0. GL + ~ l) : #. -t-0~ I-r D = .\-TJ =--I ,'. P?(+d-Z-/;:o] /~~.~~~~w (Q4) Given the function f(x,y) = _/X2 + y2 + 1; (a) [2 Marks] Find and sketch the domain of f; . ~ .. f()Y .e.vtc h (X/~) 1Y7 ~./ f(;(IJ) '-ma~ ~ .~" (?ell) IS It' f/v2 'DCf)' V) (b)[2 Marks] Find the image of f; V'i.2-tl-t1 ~/o--to-rJ ~\ =) f{;X/J):=.-/x2t-12-fJ ~-( 'K (f )~(-00 )-,1 ® (c) [4 Marks] Identify and sketch the graph of f.-2 2-;:(.Z-t'j + 2.. .=-1 J f' ;l::;. -~2-r12. .fJ ~ \ V?: /" '1-~'-\ .----._. I ~--G(f) , /...
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test2_sol_Winter_08 - (b[6 Marks Find the tangential and...

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