+564 The point of P(2,-1) lies on the curve y=1/(1-x). If Q is the point (x, 1/(1-x)), use your calculator to find the slope of the secant line PQ for the following values of x:
i) 1.5
ii) 1.9
iii) 1.99
iv) 1.999
v) 2.5
For parts i and ii of the question, I keep on getting the wrong answer... Could someone please help me out with this? Help with at least just "i" least would be appreciated.
+129899 I'll do the first one, the others are similar....(only the values have changed to protect the innocent...)
For, 1.5, we have the point on the curve
f(1.5) = 1 /(1 - 1.5) = 1 / (-.5) = -2
So we have two points (2, -1) and (1.5 , -2) and the slope of the secant line is [-2 - (-1)] / [1.5 - 2] = -1 / -.5 = 2
Here's the graph, here......note that the secant line drawn with these two enpoints would have a positive slope.
The point of this exercise is that is to show that the closer we get to x = 2, the more the secant line models the tangent line to the function at that point (i.e., the "derivative" at that point)
Hope this helps...
+129899 I'll do the first one, the others are similar....(only the values have changed to protect the innocent...)
For, 1.5, we have the point on the curve
f(1.5) = 1 /(1 - 1.5) = 1 / (-.5) = -2
So we have two points (2, -1) and (1.5 , -2) and the slope of the secant line is [-2 - (-1)] / [1.5 - 2] = -1 / -.5 = 2
Here's the graph, here......note that the secant line drawn with these two enpoints would have a positive slope.
The point of this exercise is that is to show that the closer we get to x = 2, the more the secant line models the tangent line to the function at that point (i.e., the "derivative" at that point)
Hope this helps...
