Calculus and Vectors

Knowledge/Understanding Multiple Choice: 1. Determine a . b given thata = (2, -7) and b = (-3,6) a) -36 b) -48 c) 48 d) 36 2. 3(2u - 3v) - 2(v - 5u) -4u simplified is: a) 16u - 150 b) 4u - 30 c) -3u - 67 d) 16u - 110 3. The function whose graph has a slant (oblique) asymptote is: 6x2 a) y= - x3+5x by= - x4-8x+9 x4-2 x4+5 c) y=. x3+x2-1 d) b and c 4. The derivative of y = sin(7x - 4) is: a) 7cos(7x - 4) b) -7cos(7x - 4) c) cos(7x - 4) d) (7x -4)cos(7x - 4) 5. The conjugate of 2v7 - V3 is: a) V3-2V7 b) - 2V7 + v3 C) V7 + V3 d) 2V7 + V3 6. In R', the standard basis (unit) vector, k can be expressed in component form as: a) (1, 0, 0) b) (0, 1, 0) c) (0, 0, 1) d) (1, 1, 1) 7. Evaluate the following limits: lim v4 + v25 + x * +0 a) 2 + v5 b ) 3 c) +3 d) 7 8. The incorrect vector property is: a) at b = bta ba x b = b x a c) a . b = b . a d) a - b = -bta 9. If a vector is described as an airplane flying North at 400km/h, then the opposite vector can be described as: a) An airplane flying North at -400km/h b) An airplane flying South at 400km/h c) An airplane flying South at 800km/h d) Both b and c 10. For u and v, if the sign of u . v is negative, then the angle between the tail to tail vectors will be: a) 0