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show that 1-(x/2) is the tangent line approximation to 1/sq rt(1+x) near x=0

i know the formula for apprx. is y = f(a)+f'(a)(x-a) but i don't understand how to work backwards to get this.

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If f(x) is approximated by the tangent line y(x) near x = 0, then that means that:

f(0) = y(0)

f'(0) = y'(0)

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