How do you find the tangent line approximation for #f(x)=sqrt(1+x)# near #x=0# ?

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Answer 1 · 2014-09-24T04:11:03

We need to find the derivative of #f(x)#. We need to use the Chain Rule to find the derivative of #f(x)#.

#f(x)=sqrt(1+x)=(1+x)^(1/2)#

#f'(x)=(1/2)(1+x)^((1/2-1))*1#

#f'(x)=(1/2)(1+x)^((1/2-2/2))#

#f'(x)=(1/2)(1+x)^((-1/2))#

#f'(x)=1/(2sqrt(1+x))#

#f'(0)=1/(2sqrt(1+0))=1/(2sqrt(1))=1/2=0.5#