MATH 251 Lecture Notes - Lecture 6: Ds 4

P (0,3) Let f be the function given by fox) -3 cos x. As shown above, the graph of f crosses the y-axis at point P and the x-axis at point Q (a) Write an equation for the line,passing through points p and Q. (b) Write an equation for the line tangent to the graph of f at point Q. Show tbe analysis that leads to your equation (c) Find the coordinate of the point on the graph of f, between points P and Q. at which the line tangent to the graph of is parallel to line PO

The line segment joining the points (0,3) and (5,5) is revolved about the x-axis to generate a frustum of a cone. Find the surface area of the frustum using the parameterization x =うt, y t + 3 . O s t s 2. The surface area is □ square units (Type an exact answer, using π as needed )

(1 point) View the following limit as a definite integral and then evaluate that integral by the Second Fundamental Theorem of Calculus. lim ntl 7n 7l The above limit is equal to

(1 point) Find the area of the surface generated by revolving the following curve about the axis: x = r cos t, y r sin t, 0 π. Area of the surface:

(1 point) The circle x-a cos , y = a sin t, 0 (doughnut). Find its surface area. Area of the torus: t 2π is revolved about the line x-b, 0く