By Harley Flanders; Justin J Price

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**Extra resources for Calculus with analytic geometry**

**Sample text**

Therefore the graph is symmetric with respect to the line y = x. See Fig. 5b. = 48 1 . \'. (b) If x and y are interchangeable in the 2 4 6 8 10 center (5, 12), radius 13 center ( - 2, - I), radius I center (3, 3 ), through ( - 2, -4). 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.

In this chapter we shall solve the general problem of constructing tangents to graphs of functions y = /(x). This problem is far more important than it appears to be at first glance; its solution leads to the derivative, one of the most applicable ideas in mathematics. What shall we mean by the tangent to a curve y = f (x) at a point P on the graph? We sidestep this question slightly and instead look for a reasonable definition of the slope of the graph at P. Then the tangent will be simply the line through P having that slope.

It is important how many times each factor (x - r1) occurs, so we write r, < '2 < . . < r, • to show clearly each zero r1 with its multiplicity m1 • 8. Polynomials and Rational Functions 37 x Ff&. 3 Ff&. 4 Graph of y = (x - r)2(x - s� r>s Graph of y = (x - r)(x - s)(x - t� r~~
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