# Find f 7 and f 7 f 7 f 7 since 7 6 is on y f x f 7 6

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), find f ( 7 ) and f' f ( 7 ) = f' ( 7 ) = ( 7 ). . 1 7 1 7
a ( t )= lim t pi /2 a ( t )= lim t 0 +
2/21/14, 2:36 PM Chapter 2.7 HW Page 5 of 6 (d) (e) With our restriction on t , the smallest t so that a(t)=2 (f) With our restriction on t , the largest t so that a(t)=2 (g) The average rate of change of the area of the triangle on the time interval [ π /6, π /4] is (g) The average rate of change of the area of the triangle on the time interval [ π /4, π /3] is (h) Create a table of values to study the average rate of change of the area of the triangle on the time intervals [ π /6, b ], as approaches π /6 from the right. The limiting value is (i) Create a table of values to study the average rate of change of the area of the triangle on the time intervals [ a , π /3], as approaches π /3 from the left. The limiting value is a ( t )= lim pi /4 is is . . b . a . t
2/21/14, 2:36 PM Chapter 2.7 HW Page 6 of 6 6. 12/12 points | Previous Answers The solutions (x,y) of the equation x 2 + 16 y 2 = 16 form an ellipse as pictured below. Consider the point P as pictured, with x -coordinate (a) Let h be a small non-zero number and form the point Q with x -coordinate 1 +h , as pictured. The slope of the secant line through PQ , denoted s(h) , is given by the formula . (b) Rationalize the numerator of your formula in (a) to rewrite the expression so that it looks like f(h)/g(h) , subject to these two conditions: (1) the numerator f(h) defines a line of slope -1, (2) the function f(h)/g(h) is defined for h=0 . When you do this f(h)= g(h)= . (c) The slope of the tangent line to the ellipse at the point P is lim_(h->0) s(h) = 1 .