The diagram shows the curve with parametric equations $$\[ x=\ln (2 t+3), \quad y=\frac{2 t-3}{2 t+3} . \]$$ The curve crosses the $$$y$$$-axis at the point $$$A$$$ and the $$$x$$$-axis at the point $$$B$$$. Find the gradient of the curve at $$$B$$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_21 Year：2021 Question No：5(c)

Answer:

Attempt to find value of $t$ corresponding to $y=0$
Obtain $t=\frac{3}{2}$ and hence gradient is 1

Knowledge points:

1.7.1 understand the gradient of a curve at a point as the limit of the gradients of a suitable sequence of chords, and use the notations for first and second derivatives (Only an informal understanding of the idea of a limit is expected.)

2.2.1 understand the relationship between logarithms and indices, and use the laws of logarithms (excluding change of base)

Answer:

Knowledge points:

Solution:

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