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2311_2.1ClassActivitySOLUTIONS_F11

# 2311_2.1ClassActivitySOLUTIONS_F11 - MAC2311 ‘ 50 LUT[0...

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Unformatted text preview: MAC2311 ‘ 50 LUT [0 N5 2.1 Activity: Secant Lines; Tangent Lines; Average Velocity; Instantaneous Velocity - 1. The graph of f (A) — ~;contains point P(2 %). 21) Pint point P on the graph. Then use a straight— edge to sketch the tangent line at P(2,%) . b) Suppose point Q is positioned at (yﬂ). Line 135 is called asecant line. Sketch line E and calculate its slope. F042,)“ “2) ... 2%?” w M secgg 3/73.; '/2'm2. Answer: 17: = we] see M c) Rounding each answer to four decimal places if necessary, ﬁnd the slope of each secant line E if the x-coordinate of point Q is... x=1 x Ii.5 3621.9 x:1.99 x=1.999 . unite; to s") {(23 toawa) Maggi 9331:5433 “‘1' “WT???W “73'“:me ”\$.42 mama Answers: mm? —,‘S' mm; —,‘3’533 mmg «,Qtaﬁl mmg ~,'?.‘§\’b nzsccg‘F-lgbl d) Use the results of part (1) to guess the value of the slope of the tangent line at P(2,%) Answer: m = ”.25. ov—l- tan Ll' e) Use your guess from part d) to write an equation for the tangent line to the curve at P(2,%) . ymy, mmtxmxi) :25 y» 3;: z: ._ ﬁU‘ﬂ) Answer: Y ‘3 ‘“ ”14X “l" l 2. An object is dropped from the top of the CN Tower in Toronto, 450m above the ground. The object’s height above the ground (in meters) at time t seconds is given by h (f) m 450 —— 4.91!“2 . a) Over any given time interval during this experiment the average velocity of the object will be negative because height is a decreasing quantity. Calculate the average velocity of the object over each time interval. Round to three decimal places as needed, and use correct units in each answer. 3<t<4 3<t<3.5 3933.1 3953.01 so: he? News}. blirillité? resin? 4 3 3.9% .3.l=~3 3.0\e\$ Answers: vm = w3‘i,’ﬁ E; em = ”\$387; 'E van, 2 «~29. 891m vm, : a 23' [+5 £9... 3 s S 5 b) Use the results of part a) to guess the instantaneous velocity of the object at 2‘ = 3 seconds. Record the answer with correct units. Answer: Nate: Overs Bet-é 3.094 ' NJ Over ’3 e l; .4:- 3.00m a, Vawe '33 “2%.40qu Vavg ‘3. mQﬁ§rOOqu gear“; it kérv WQFFﬂJaa’um “2-61. QM ? N “Lake, “lends viewer”: 3 wreceeclie . As we, wrll Seem iéiﬂlvt‘ﬁ’ «w, ‘mstamianeone velodira all” its? me les‘ZﬂiJ—rmg. Tlauﬁl "ll/m eioJeef’i IS ‘ir’muelim j downwewci of as. asee; ﬁg .Zﬁ Ltrn/ oil “lame “it”? 3 reewgg ...
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