Linear Approximation Question

Question

So I was given this question:

Use the linear approximation to $f(x, y) = \sqrt{\frac {x+5} {y+2}}$ at $(2, 3)$ to estimate $\sqrt \frac {7.1} {4.9}$.

I was able to get the actual value by just doing the $\sqrt{7.1 / 4.9}$ which was $1.203735$. But, I tried getting the estimated value, and by extension the percent error, but ultimately failed. Can someone please help?

https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference — Xander Henderson, Mar 14 '19 at 19:14
I presume this is for Calc 3 - have you been going to lectures? See Example 2 of http://tutorial.math.lamar.edu/Classes/CalcIII/TangentPlanes.aspx — DanLewis3264, Mar 14 '19 at 19:22

score 3 · Accepted Answer · answered Mar 14 '19 at 19:19

3

You can use Taylor's formula

$$ \sqrt{7.1/4.9} = f(2+0.1,3-0.1)\approx f(2,3) + 0.1 f'_x(2,3)-0.1 f'_y(2,3) $$

Of course, to use this formula you must know or be able to estimate $f(2,3), f'_x(2,3)$ and $f'_y(2,3)$.

answered Mar 14 '19 at 19:19

PierreCarre

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Linear Approximation Question

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