Course:MATH102/Question Challenge/2008 December Q2c

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Question

The following problems require little or no computation. Put the answer in the box provided. You may use space here for supporting reasoning or computations, if any, for which part-marks would be awarded.

(c) A linear approximation for $y=\sin(0.05)$ that uses the fact that $\sin(0)=0$ is

$\sin(0.05)\approx$

Hints

Hint
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Solutions

Solution
$f(x)=\sin x$ $f(x)\approx f(x_{0})+f'(x_{0})\cdot (a-x)=\sin(0)+\cos(0)\cdot (0.05)=0+1\cdot (0.05)=0.05$