A research drone monitors the rate of data transmission, D(t)D(t)D(t), in gigabits per hour, from a remote sensor over a 4-hour period. The transmission rate is modelled by the function
D(t)=1.25t0.5t2+4,0≤t≤4 D(t) = \frac{1.25^t}{\sqrt{0.5t^2 + 4}}, \quad 0 \le t \le 4 D(t)=0.5t2+41.25t,0≤t≤4Complete the table below, giving the values of D(t)D(t)D(t) to 3 decimal places.
| ttt | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| D(t)D(t)D(t) | 0.500 | 0.638 | 0.705 |
Use the trapezium rule, with all the values of D(t)D(t)D(t) from the completed table, to find an approximate value for the total data transmitted,
∫041.25t0.5t2+4 dt \int_{0}^{4} \frac{1.25^t}{\sqrt{0.5t^2 + 4}} \, dt ∫040.5t2+41.25tdt137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.