1.40: Graph of a logarithmic function and root estimation

4PM1/1R/June/2019 — Question 8 · 11 marks

(a) Complete the table of values for

y=2+\ln(2x+1)

giving your answers to 2 decimal places.

$x$	$0$	$0.25$	$0.5$	$1$	$1.5$	$2$	$3$
$y$	$2$			$3.10$	$3.39$	$3.61$

(2)

(b) On the grid opposite, draw the graph of

y=2+\ln(2x+1)

for

0\leqslant x\leqslant 3

(2)

(c) By drawing an appropriate straight line on the grid, obtain an estimate, to one decimal place, of the root of the equation

\ln(2x+1)=3x-4

in the interval

0\leqslant x\leqslant 3

(3)

(d) By drawing an appropriate straight line on the grid, obtain an estimate, to one decimal place, of the root of the equation

\mathrm{e}^{(6-x)}-(2x+1)^{2}=0

in the interval

0\leqslant x\leqslant 3

(4)