Calculus and Vectors

True or False: |2 Marks]| 29. The derivatives helps us determine the rate of change. 30. We set the derivative equal to zero to find the slope. 31. Match the Definitions (write the corresponding letter in the space provided) a) Coincident b) Collinear Vectors ) Continuity d) Coplanar ) Cross Product f) Dot Product g) Critical Numbers h) Derivative 1) Direction Vector ) Equilibrium k) Resultant 1) Force m) Geometric Vectors n) Linear Combination 0) Magnitude p) Normal Axis q) Normal Line r) Optimize s) Projection t) Vector u) Position Vector 1. : the sum of two or more vectors; represents the combined effect of the vectors ii. : the absolute value of a quantity 11l. : to realize the best possible outcome for a situation, subject to restrictions. v. : a quantity that requires both a magnitude and a direction for a complete description. V. : the line drawn at a point on a graph of f(x), perpendicular to the tangent line drawn at that point. V1. : the sum of nonzero multiples of two of more vectors or equations. Vil. : numbers in the domain of a function that cause its derivative to be zero or undefined. 32. Determine the vector equation of the plane that contains the following two lines. . L1: =[4,-3, 5] +t[2,0,3],t R and L2: =[4,-3, 5] +s[5,1,-1],s ER 33. Sketch the diagram that you would use to find the magnitude of the sum of @ and b if the angle between them is 67" and the magnitudes are 7 and 11 respectively. Ensure that all vectors are labelled. Also include the equilibrium vector in your diagram. ! 34. For the function whose graph is given below, find the following: a. llIP f(x)= b. lirg;f(x]: . 1in;1f(x]: d. lirrjl_f(x}: e. lirrjl_f(x}z f. limlf(x} - g Jf(@2)= h S(D=