Question

The point P(8, -4) lies on the curve y = 4/(7 - x). (a) If Q is the point (x, 4/(7 - x)), use your calculator to find the slope mpQ of the secant line PQ (correct to six decimal places) for the following values of x. (i) 7.9 mpQ =

(ii) 7.99 mpQ =
(iii) 7.999 mpQ =
(iv) 7.9999 mpQ =
(v) 8.1 mpQ =
(vi) 8.01 mpQ =
(vii) 8.001 mpQ =
(viii) 8.0001 mpQ =

Answer 1

To find the slope of the secant line PQ, we need to find the slope between points P and Q. The slope between two points is given by the formula: m = (y2 - y1) / (x2 - x1).

Step-by-step explanation:

To find the slope of the secant line PQ, we need to find the slope between points P and Q. The slope between two points is given by the formula: m = (y2 - y1) / (x2 - x1).

Let's calculate the slopes for each value of x:

1. x = 7.9: m = (4/(7-7.9) - (-4))/(7.9-8) ≈ 0.833333
2. x = 7.99: m = (4/(7-7.99) - (-4))/(7.99-8) ≈ 0.830189
3. x = 7.999: m = (4/(7-7.999) - (-4))/(7.999-8) ≈ 0.830084
4. x = 7.9999: m = (4/(7-7.9999) - (-4))/(7.9999-8) ≈ 0.830079
5. x = 8.1: m = (4/(7-8.1) - (-4))/(8.1-8) ≈ 0.839286
6. x = 8.01: m = (4/(7-8.01) - (-4))/(8.01-8) ≈ 0.830517
7. x = 8.001: m = (4/(7-8.001) - (-4))/(8.001-8) ≈ 0.830083
8. x = 8.0001: m = (4/(7-8.0001) - (-4))/(8.0001-8) ≈ 0.830079

The slopes of the secant line PQ for the given values of x are approximately: 0.833333, 0.830189, 0.830084, 0.830079, 0.839286, 0.830517, 0.830083, and 0.830079.