3.3.7 Sequences and series (A-level only)

Question 9

A precise micro-sensor measures the relative volume $V\,$ of a specialized crystal alloy as it undergoes temperature changes $T$ . The relationship is modelled by the formula $\sqrt[3]{1 + pT}$ , where $p\,$ is a constant. The binomial expansion of $V (T)$ in ascending powers of $T$ , up to the term in $T^3$ , is $1+16T+CT2+DT3\displaystyle 1 + \frac{1}{6}T + CT^2 + DT^3$ for $∣ pT ∣ < 1$ .

a.

(i) Find the value of $p$ .

(ii) Find the values of the constants $C\,$ and $D$ .

[5]

b.

Use the expansion to find an approximate value for $1.13\sqrt[3]{1.1}$ , showing your working and giving your answer to 6 decimal places.

[4]

3.3.7 Sequences and series (A-level only)

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Question 9

A precise micro-sensor measures the relative volume $V\,$ of a specialized crystal alloy as it undergoes temperature changes $T$ . The relationship is modelled by the formula $\sqrt[3]{1 + pT}$ , where $p\,$ is a constant. The binomial expansion of $V (T)$ in ascending powers of $T$ , up to the term in $T^3$ , is $1+16T+CT2+DT3\displaystyle 1 + \frac{1}{6}T + CT^2 + DT^3$ for $∣ pT ∣ < 1$ .

a.

(i) Find the value of $p$ .

(ii) Find the values of the constants $C\,$ and $D$ .

[5]

b.

Use the expansion to find an approximate value for $1.13\sqrt[3]{1.1}$ , showing your working and giving your answer to 6 decimal places.

[4]

3.3.7 Sequences and series (A-level only)

Question 9

3.3.7 Sequences and series (A-level only) Questions

3.3.7 Sequences and series (A-level only)

Question 9

3.3.7 Sequences and series (A-level only) Questions