By Harley Flanders; Justin J Price
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Extra resources for Calculus with analytic geometry
8) " 0, y Answer 0. becomes very steep (Fig. ). f(x), a. f (a)) and Q,. f(a + h)). Compute the slope of the secant through P and Q,. 01 I lr = O. r = f(x) at (-2, 12). ) Now compute the slope of = f (x) at (0, 0). x ) = 2x2 + l'< 9 ,, = -0. 1 - . 00 1 II Ir = - I0- 5. 2. ) Now compute the slope of y = f (x) = xl + 59 f(x) at (2. 14). l� /(x) at ( I, 2). ,, = - I0- 1 0. 000 1 . ) Now compute the slope of y = /(x) at (4. 61). 21 Compute the slope of y = 3x2 at (a. 3a2). 22 Compute the slope of J' = x2 - x at (a, a1 - a).
Center (I, 2� tangent to x-axis diameter from (-2, -3) to (4, I ). equation y = f(x), then the graph is symmetric in the line y = x. EXERCISES Write the equation or the circle 1 center (I, 3), radius 6 3 center ( -4, 3), radius 5 S center (I, 5), through (0, 0) 7 center ( - 5, 2), tangent to y-axis 9 diameter from (0, I ) to (3. 3) Write the equation for the most general circle. 1 1 radius 3, tangent to x-axis 12 center in first quadrant, tangent to both axes 13 passing through (0, 0) 14 tangent to the line )' = 3.
In each case we introduce the auxilliary point (x 2 , y1� forming a right triangle as shown. The legs have lengths l x2 - x1 I and I Y2 - Ya I. so by the Pythagorean theorem, I. d2 = l x2 - x a l2 + I Y2 - Ya l 2 = (x2 - x a )2 + (y2 - Ya )2. Distance Formula The distance between J(x 2 - x a )2 + (Y2 - (x a , Ya ) and (x2 , y2 ) is }1a)2 . 1 . FU NCT I O NS A N D GRAPHS 44 ,- I I I ( \" 1 • r-1 --� '1 ) r-1 ___ 4 , ,� · ' • , (\ � I I l (\I ' I F'11- I I l I , • Distance between points horizontal line or the sameanverti cal line,point.