Mathematics, 30.03.2020 21:49, Felixthecat8241
Find the linear approximation of the function g(x) = 3 1 + x at a = 0. g(x) ≈ Use it to approximate the numbers 3 0.95 and 3 1.1 . (Round your answers to three decimal places.) 3 0.95 ≈ 3 1.1 ≈
Answers: 3
![\sqrt[3]{0.95} \approx 0.983\\\\\\\sqrt[3]{1.1} \approx 1.033](/tpl/images/0571/4144/b021a.png)
![g(x) =\sqrt[3]{1+x}](/tpl/images/0571/4144/c2645.png)
![g(a)=g(0)=\sqrt[3]{1+0}=1](/tpl/images/0571/4144/88bc7.png)
![g'(x)=\frac{d}{dx}[(1+x)^ {1/3}]=(1/3)(1+x)^{-2/3}=\frac{1}{3(1+x)^{2/3}}](/tpl/images/0571/4144/b2fda.png)
![\sqrt[3]{0.95}](/tpl/images/0571/4144/388c5.png)
![0.95=1+x\rightarrow x=-0.05\\\\\sqrt[3]{0.95} \approx 1+\frac{(-0.05)}{3} =1-0.017=0.983](/tpl/images/0571/4144/c7e2b.png)
![\sqrt[3]{1.1}](/tpl/images/0571/4144/3414f.png)
![1.1=1+x\rightarrow x=0.1\\\\\sqrt[3]{1.1} \approx 1+\frac{(0.1)}{3} =1+0.033=1.033](/tpl/images/0571/4144/aee9f.png)
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Find the linear approximation of the function g(x) = 3 1 + x at a = 0. g(x) ≈ Use it to approximate...
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