?? - 2016 Q4 ANSWERS
4.
Figure 1 shows a sketch of part of the curve with the equation y=g(x), where
g(x) = |4e2x - 25|
The curve cuts the y-axis at the point A and meets the x-axis at the point B. The curve has an asymptote y = k where k is a constant as shown in Figure 1
(a) Find, giving each answer in its simplest form,
(i) the y coordinate of the point A,
(ii) the exact x coordinate of the point B,
(iii) the value of the constant k. (5)
The equation g(x) = 2x + 43 has a positive root at x = a
b) Show that a is a solution of x = 0.5 ln (0.5x + 17) [2]
The iteration formula
xn+1 = 0.5 ln (0.5x + 17)
can be used to find an approximation for a
c) Taking x0 = 1.4 find the values of x1 and x2
Give each answer to 4 decimal places. [2]
(d) By choosing a suitable interval, show that a = 1.437 to 3 decimal places (3)
The curve cuts the y-axis at the point A and meets the x-axis at the point B. The curve has an asymptote y = k where k is a constant as shown in Figure 1
(a) Find, giving each answer in its simplest form,
(i) the y coordinate of the point A,
(ii) the exact x coordinate of the point B,
(iii) the value of the constant k. (5)
The equation g(x) = 2x + 43 has a positive root at x = a
b) Show that a is a solution of x = 0.5 ln (0.5x + 17) [2]
The iteration formula
can be used to find an approximation for a
c) Taking x0 = 1.4 find the values of x1 and x2
Give each answer to 4 decimal places. [2]
(d) By choosing a suitable interval, show that a = 1.437 to 3 decimal places (3)