Mathematics, 20.09.2019 10:30 carapiasebas
Find a linear approximation of the function f(x)=\sqrt[3]{1+x} at a=0, and use it to approximate the numbers \sqrt[3]{.96} and \sqrt[3]{1.02}
Answers: 1
![f(x)=\sqrt[3]{1+x}=(1+x)^{1/3}\implies f'(x)=\dfrac1{3(1+x)^{2/3}}](/tpl/images/0246/0447/4d578.png)
around 
is then
will be
![\sqrt[3]{0.96}\approx L(0.96)=1+\dfrac{0.96}3=1.32](/tpl/images/0246/0447/b7b20.png)
![\sqrt[3]{1.02}\approx L(1.02)=1+\dfrac{1.02}3=1.34](/tpl/images/0246/0447/6f085.png)
![\sqrt[3]{0.96}\approx0.9864](/tpl/images/0246/0447/323bf.png)
![\sqrt[3]{1.02}\approx1.0066](/tpl/images/0246/0447/9a063.png)
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Find a linear approximation of the function f(x)=\sqrt[3]{1+x} at a=0, and use it to approximate the...
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