The equation of a curve is $$\(y=(x-3) \sqrt{x+1}+3\)$$. The following points lie on the curve. Non-exact values are rounded to 4 decimal places. $$\[ A(2, k) \quad B(2.9,2.8025) \quad C(2.99,2.9800) \quad D(2.999,2.9980) \quad E(3,3) \]$$ The gradients of $$\(B E, C E\)$$ and $$\(D E\)$$, rounded to 4 decimal places, are $$\(1.9748,1.9975\)$$ and $$\(1.9997\)$$ respectively. State, giving a reason for your answer, what the values of the four gradients suggest about the gradient of the curve at the point $$\(E\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_s21_qp_12 Year：2021 Question No：3(c)
Answer:
Sight of 2 or \(2.0000\) or two in reference to the gradient
This is because the gradient at \(E\) is the limit of the gradients of the chords as the \(x\)-value tends to 3 or \(\partial x\) tends to 0 .
This is because the gradient at \(E\) is the limit of the gradients of the chords as the \(x\)-value tends to 3 or \(\partial x\) tends to 0 .
Knowledge points:
1.3.2 interpret and use any of the forms in solving problems (Including calculations of distances, gradients, midpoints, points of intersection and use of the relationship between the gradients of parallel and perpendicular lines.)
Solution:
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