MATH 233-2, Spring 2017 Nume: - Quiz 7 Due Feb. 16, 2017 Show all work clearly. Justify your answers algebraically whenever possible. Wlwn you u: w a calculator, sketch all relevant graphs and write down all of your computations. 1. Let C be the space curve defined by the vector function u(t) on the domain I- l, l:, wlwrv u(t) = . (a) Find a quadric surface S that contains C and write an equation for it. Hint: label the component functions of u(t) as x,y,z. Can you find a quadratic eqzviatwn HI cc, y, z that is always satisfied for every value of it? You may need to use a simple trig. identity. (b) Write parametric equations for the tangent line to C at the point u(0). Hint: First find a point on this line and a direction vector for it. (c) What does C look like? Try to draw a picture of S and C. You may want to use a computer program like grapher, Sage, or wolframalpha. com to help you visualize them