Study Pure Mathematics notes on Differentiation for A-Level. Useful for revision, homework, and exam preparation in Zimbabwe.
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A' LEVEL
PURE MATHEMATICS
DIFFERENTIATION TEST 7
SOLUTION
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Sharewell B. C
1. Using $\boldsymbol{y}=\sqrt[3]{x}$ find, without using a calculator, an approximate value for;
a) $\sqrt[3]{9}$
[3]
b) $\sqrt[3]{63}$
[3]
SOLUTION
a) $y=\sqrt[3]{x}$
\[
\Rightarrow \quad \frac{d y}{d x}=\frac{1}{3}(x)^{-\frac{2}{3}}
\]
\[
\delta y=\frac{d y}{d x} \delta x \quad \text { gives } \quad \delta y \approx \frac{1}{3(\sqrt[3]{x})^{2}} \delta x
\]
Now, taking the value with an exact cube root.
\[
\begin{array}{l}
x=8, \quad y=\sqrt[3]{8} \quad \text { and } \quad \delta x=1
\delta y \approx \frac{1}{3(\sqrt[3]{8})^{2}}(1)
\end{array}
\]
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