Question 62 – 3.7 Numerical methods (A-level only) - Questions

The gain response, $G$ , of a specialized amplifier is modeled by the function $G(t) = \log_2(4t)$ , where $t$ is the signal frequency in kHz. The table below shows values of $G$ for specific frequencies recorded during a test.

$t246810G3.004.004.585.005.32\begin{array}{|c|c|c|c|c|c|} \hline t & 2 & 4 & 6 & 8 & 10 \\ \hline G & 3.00 & 4.00 & 4.58 & 5.00 & 5.32 \\ \hline \end{array}$

Using the trapezium rule with all the values of $G$ in the given table,

obtain an estimate for $dt\int_{2}^{10} \log_2(4t) \, dt$ , giving your answer to one decimal place.

Using your answer to part (a) and making your method clear, estimate

(i) $dt\int_{2}^{10} \frac{\log_2(64t^3)}{5} \, dt$

(ii) $dt\int_{2}^{10} \log_2 \left(\frac{16}{t}\right) \, dt$

$t246810G3.004.004.585.005.32\begin{array}{|c|c|c|c|c|c|} \hline t & 2 & 4 & 6 & 8 & 10 \\ \hline G & 3.00 & 4.00 & 4.58 & 5.00 & 5.32 \\ \hline \end{array}$

Using the trapezium rule with all the values of $G$ in the given table,

obtain an estimate for $dt\int_{2}^{10} \log_2(4t) \, dt$ , giving your answer to one decimal place.

Using your answer to part (a) and making your method clear, estimate

(i) $dt\int_{2}^{10} \frac{\log_2(64t^3)}{5} \, dt$

(ii) $dt\int_{2}^{10} \log_2 \left(\frac{16}{t}\right) \, dt$

3.7 Numerical methods (A-level only)

Question 61

3.7 Numerical methods (A-level only)

Question 61

3.7 Numerical methods (A-level only)

Question 61

3.7 Numerical methods (A-level only) Questions

3.7 Numerical methods (A-level only)

Question 61

3.7 Numerical methods (A-level only) Questions