MATH 1172 Midterm: MATH 1172 Ohio State University Math 1172 11.1 Solutions Fa 2014

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

16x 6 16: find a parametric equation of the circle centered at (2, 4) with radius 2 generated clockwise. Solution: x(t) = 2 + 2 cos( ) y(t) = 4 2 sin( ). dx in terms of t. then nd all points. Find dy (x, y) on the curve at which there is a horizontal tangent line. Solution: using the chain rule, we can express dy/dx in terms of dy/dt and dx/dt: dy dx dy/dt dx/dt. Points with a horizontal tangent line are points where the slope dy/dx is 0: 3t2 12 = 0 t2 = 4 t = 2: consider the parametric x = t, y = 4t. Find dy/dx in terms of t and evaluate the derivative at t = 3. So the points corresponding to t = 2 will have horizontal tangent lines. Plugging in t to nd x and y, we get the two points.