1.13: Complete the table of values for y = 2x + 1 + 2/x²

4PM1/2R/November/2020 — Question 4 · 11 marks

(a) Complete the table of values for

y = 2x + 1 + \frac{2}{x^2}

Give your answers to 2 decimal places where appropriate.

$\displaystyle x$	$\displaystyle 0.5$	$\displaystyle 1$	$\displaystyle 1.5$	$\displaystyle 2$	$\displaystyle 2.5$	$\displaystyle 3$	$\displaystyle 3.5$
$\displaystyle y$		$\displaystyle 5$			$\displaystyle 6.32$		$\displaystyle 8.16$

(2)

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

y = 2x + 1 + \frac{2}{x^2} \quad \text{for} \quad 0.5 \leq x \leq 3.5

(2)

2x + \frac{2}{x^2} = 7 \quad \text{in the interval} \quad 0.5 \leq x \leq 3.5

(2)

(d) By drawing a suitable straight line on the grid, obtain estimates, to 1 decimal place, of the roots of the equation

\frac{3x}{2} + \frac{2}{x^2} = 5 \quad \text{in the interval} \quad 0.5 \leq x \leq 3.5

(5)