Question Three 1 In Calculus The Curvature Of A Curve Whose Equation Is By Y F X Is Defined To Be The Number K 1 (56.29 KiB) Viewed 73 times
Question Three:- (1) In calculus the curvature of a curve whose equation is by y = f(x) is defined to be the number k = y"/[1 + (y¹²]³/². Determine a function for which k = 1. [ Hint: For simplicity ignore constants of integration. Also consider a trigonometric substitution.] (2) According to Stefan's law of radiation, the rate of change of temperature from a body at absolute temperature Tis dT dt = K (T¹ – T₁), (2) where To is the absolute temperature of the surrounding medium. Find a solution of Eq. (2) It can be shown that when T - To is small compared to To that this particular equation is
closely approximated by Newton's law of cooling. (3) Solve the differential equation of the tractrix dy dx Assume that the initial point on the y-axis is (0, 10) and the length of the rope is s = 10 ft. y 05
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