Approximating solutions to equations

12 questions

1. What is 0.0647399 rounded to 2 significant figures?
2. What is the value of the expression x^3 +3x-12 when x=2?
3. For which values of x are we able to evalate the expression \sqrt{6-2x}?
4. Use the iterative formula P_{t+1}=2.5(P_t-50) with P_0=200 to find the value of P_4. Write down your full calculator display.
5. Using the iterative formula x_{n+1}=10-4(x_n) with x_0=1 which of these is the value of x_8?
6. Using the iterative formula x_{n+1}=\sqrt{10-2(x_n)} and x_0=3 match up the iterations with their values.
7. Which value does the iterative formula x_{n+1}=\frac{5}{x_n}-3 converge on to 1 significant figure when x_0=2 ?
8. Which value does the iterative formula x_{n+1}=\frac{5}{x_n}-3 converge on to 2 significant figures when x_0=2 ?
9. How can we tell if an iterative formula is converging for a given value of x_0?
10. Which of these could be an iterative formula to find a solution to x^3-3x-5=0 ?
11. To find a solution to the equation x^3+6x-10=0 the iterative formula x_{n+1}=\frac{10-(x_n)^3}{6} can be used. Using x_0=1 find the value of x_3
12. Using the iterative formula x_{n+1}=\frac{10-(x_n)^3}{6} and x_0=1 there is a solution to x^3+6x-10=0 correct to 2 significant figures when x=___

License: OGL