How do you find the linear approximation of the function #g(x)=root5(1+x)# at a=0?

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Answer 1 · 2016-12-30T13:22:29

#root(5)(1+x) ~= 1+x/5#

The best linear approximation of #g(x)# around #x=0# is its tangent line:

#y(x) = g(0)+g'(0)x#

Given that:

#g(x) = root(5)(1+x) = (1+x)^(1/5)#

#g'(x) = 1/5(1+x)^(-4/5)#

we have:

#g(0) = 1#

#g'(0) = 1/5#

so:

#root(5)(1+x) ~= 1+x/5#

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