Mathematics, 19.09.2019 18:30 sloane50
The point p(1,1/2) lies on the curve y=x/(1+x). (a) if q is the point (x, x/(1+ find the slope of the secant line pq correct to four decimal places for the following values of x: (1) .5 (2) .9 (3) .99 (4) .999 (5) 1.5 (6) 1.1 (7) 1.01 (8) 1.001
Answers: 1
lies on the curve.
is an arbitrary point on the curve.![\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\frac{x}{1+x}-\frac{1}{2}}{x-1}=\dfrac{\frac{2x-(1+x)}{2(x+1)}}{x-1}=\dfrac{\frac{2x-1-x}{2(x+1)}}{x-1}=\\ \\=\dfrac{\frac{x-1}{2(x+1)}}{x-1}=\dfrac{x-1}{2(x+1)}\cdot \dfrac{1}{x-1}=\dfrac{1}{2(x+1)}\ [\text{When}\ x\neq 1]](/tpl/images/0243/6980/787e4.png)
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The point p(1,1/2) lies on the curve y=x/(1+x). (a) if q is the point (x, x/(1+ find the slope of th...
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