AC2313 Sample 2 a) Find the domain of (t) b) Sketch the domain in 2-space c) lim

Question

AC2313 Sample 2 a) Find the domain of (t) b) Sketch the domain in 2-space c) limC) Find the vector equation from P to Q where P/1, 2,-2), Q(3,-1,4) Find the vector function in parametric form that represents the curve of intersection of surfaces z = x2 + 4y2 and y = x2 Given i(t) = (t + 1, t2-2, t*) find a) F(t) b) t1 . 3. 4. 1) 5. 6. Find the equation of the line tangent to x-t sint, y st, z-t cost at the point (0, ,-n) Find the arc length off(t)s sint 1+-+ cost k from (0,0 , 1) to (0, 2r. 1) 7. Given curvature to ol find the curvature of FO) (2,2t, e3) at C 8. Find N(t) and B(t) for the equation in #6 at the point (1, /2 9. Given the position vector r(t) = (et,e2tt) find the velocity, acceleration and speed 10. Show the following limits do not exist a) lim (x,y)-(0,0) x4+y2 lim- (x,y)-(0,0) x yt b) 11. Evaluate (xyim(3,2)xy + 2y-xy2 2. Given f(x,y) = xy + 2y-xy2 find: a)3,2) b) f,(3,2) c) frx (3,2) d) fyy (3,2) e) fay (3,2) f fx (3,2) 3. Find the equation of the plane tangent to fx.y) in number 12 at (3, 2, 12)

Explanation / Answer

P(1,2,-2) Q(3,-1,4)

(x,y,z)=P+t(PQ)

t is a parameter

(x,y,z)=(1,2,-2)+t(-2,3,-6)

(x,y,z)=(1-2t,2+3t,-2-6t)

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