MATH 251 WEEK 3 RECITATIDN SPRING 2022 5 1 Determine the derivative of r 2 x? - I + r r 1+ 1 5 1 {2} Differentiate y = 51." + E {3} Let 9(3) = 41:3 - 63:2 Br + 4. {a} Find the tangent line to 3(3) at the point :r = 1. {b} Use the tangent line to approximate g[1.5} {c} Compute the value of y[1.5}. How accurate was the estimate you found in part {b}? {4} Some students were trying to nd the derivative of 311:1} = 39(3) fLr). They have already determined that f'[1.'} = are1 and 53(3) = 23:2 - 5. Finish the problem by nding 3111'}. {5} A mathematical model for vertical height of a stone that is dropped from a height of [34 feet above the ground is: SH} = -l'l5it2 + '54 The function s[t} gives the height of the stone measured in feet [ft] above the ground as a function of time i measured in seconds (s). {a} 1What is the average velocity of the stone over the interval [1,2] [between 1 and 2 seconds after it is dropped}? {b} 1What is the equation for the velocity of the stone as a function of time? (c) 1What is the equation for the speed of the stone as a function of time? (Speed is the absolute value of velocity.) {d} How long does it take for the stone to reach the ground? (e) 1What is the velocity of the stone when it hits the ground