1. Given o. o} = e\" + o Inlosll. nd the following and make sure you simplify your answers! {a} mm: {b} Elie. In) 2. Let x. y] = 4:33p: + 333293, nd: {a} vftis} {h} f?\" . 2}. where I = g? _ {- 3. In a room, the temperature is given b3..- 1" 2 flag} degrees C915ju5 where I gives the distance from the heater I: in meters] and t is the elapsed time [in minutes] since the heat has been turned on. A. person standing 5 meters from the heater 3 minutes after it has been turned on observes the following: {1] At this distance, the temperature is increasing by 2: C per minute. and [2] 'v'v'alking awav from the heater, the temperature decreases bv 1236' per meter as time is held constant. Estimate how much colder or warmer it would be 6 meters from the heater after 2.5 minutes. 4. Consider the surface with equation 43:2 33;? + :2 = 25 {a} Find a vector normal to the surface at [3.2.1]. {b} Find the equation of the tangent plane at the point {3.2.1}. 5. Please do all parts ac. {a} Find a unit vector E. having the same direction as: 371 + Ij. {b} Find the measure of the angle between E =-.. 4. 3. 1 and b =:.' l. 2. 2 {c} Find p. x t: given 3 =4; 1. i. 2 and E =4; 1.i.2 6. Suppose that the depth. h. of a lake below the point {my} on the surface is given by blimp} = lry 2:3 20. The point {my} is the location of the duck on the surface of the lake where 9.: and y are measured in feet on the surface of the lake and h is the depth. measured in feet below the point {3.3;}. Suppose a duck is at the point {3. 2]. {a} What will the instantaneous rate of change in the depth of the lake if the duck heads in the direct-ion towards the point {6T}? Will the depth be increasing or decresing'.r No decimals in your answer please {in other words, provide an EXACT answer}. {b} In what direct-ion should the duck swim from the point {3. 2] in order for the depth to decrease most rapidly? Your answer should be in vector format. [c] How fast will the depth increase in the direction given in Part b? No decimals in vour answer please [in other words. provide an EXACT answer}. {d} In what direct-ion should the duck swim so that the depth remains the same'.r