Question
Find the linear approximation at $x=0$ to show that the following commonly used approximations are valid for "small" $x .$ Compare the approximate and exact values for $x=0.01, x=0.1$ and $x=1$$$\sqrt{4+x} \approx 2+\frac{1}{4} x$$
Step 1
This is done by substitifying $x=0$ into the function $\sqrt{4+x}$: $$f(0) = \sqrt{4+0} = 2$$ Show more…
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