calc exam 1

# calc exam 1 - Average Velocity =(S2-S1(t2-t1...

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Average Velocity = (S2-S1)/(t2-t1) = ((S2(t)) –(S1(t))) ÷ ((t2)-(t1)) (2 × 8% = 16%) At time t, in seconds, a particle moving along a line has coordinate s(t) = t 2 + 4 t − 2, in meters. () Calculate the particle’s average velocity over the time interval [3, 3.1]. Give your answer as a single number with appropriate units. ((3.1)^2 + 4(3.1)-2) - ((3)^2 + 4(3)-2) ÷ ((3.1)-(3)) = (9.6+12.4 -2)÷(0.1) = 20.01-19÷ (0.1) = 1.01÷ 0.1 = 10.1m/s () Calculate the particle’s average velocity over the time interval [3, 3+∆t] where _t > 0. Simplify your answer. ((3+∆t)^2 + 4(3+∆t)-2) - ((3)^2 + 4(3)-2) ÷ ((3+∆t)-(3)) Remember (a+b)^2 = a^2+2ab+b^2 ((3^2 + 2(3) ∆t +(∆t)^2) +(4(3)+4∆t) -2 ) – ((-3^2 -4(3)+2 )÷ (∆t) = (10 + ∆t) Vertical and Horizontal asymptotes Consider f(x) = 3x^ 2 + 1 ------------ X^ 2 − 9 . () By calculating relevant limits, determine the equations of all verticalasymptotes of the graph of f(x). If there are none say X= a if Lim f(x) = + or – INFINITY ,x-
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