MAT135H1 Lecture Notes - Lecture 14: Maxima And Minima

4. Suppose a red-hot steel rod is plunged into a bath of cool water. Let Tlt) be the temperature of the rod at time t, and suppose the water is maintained at a constant temperature of 10 degrees Celsius. If you know that the rate of change of temperature with time is proportional to the difference of the temperatures between the rod and the water, find an expression on how does the temperature of the rod changes with time?

P-S+(1/2)T L-C-P+S G-R S-T M-2T+G-L 2R-2M-C-L CIL+G-SHR M-P+(3/2)1

16)Find the curvature K at the point P. a)r(t)=( 1/2t^2,t,1/3 t^3) P(1/2,1,1/3) b)r(t)=(4cos(t),3sin(t),t) P(-4,0,pi)