MATH 104 Midterm: MATH104 Midterm 2011 Winter

• School: UBC
• Department: Mathematics
• Course: MATH 104
• Professor: All

Document Summary

Show all your work; little or no credit will be given for a numerical answer without the correct accompanying work. If you need more space than the space provided, use the back of the previous page. Where boxes are provided for answers, put your nal answers in them. Rules governing examinations: each candidate must be prepared to produce, upon request, a. Consider the curve given by y2 + 2xy + x3 = 4 (a) evaluate dy dx at the points (x, y) = (1, 1) and (1, 3). Use implicit di erentiation to evaluate dy/dx y2 + 2xy + x3 = 4 dy dx. + 2x dy dx dy (2y + 2x) dx. 4 (b) find the equations of the tangent lines to the curve at the points (x, y) given in a). Using the answer from part a) for the slopes of the tangent lines, we just make the appropriate substitutions into the tangent line formula;