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Let the variable xn, be determined by th...

Let the variable `x_n`, be determined by the following law of formation 0`x_0=sqrt(a)x_0=sqrt(a),x_1=sqrt(a+sqrt(a))x_2=sqrt(a+sqrt(a+sqrt(a))) and x_3=sqrt(a+sqrt(a+sqrt(a+sqrt(a))))` then find `lim_(n->oo) x_n`.

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if f(x)=sqrt(x+sqrt(x+)sqrt(x+)sqrt(…oo)),

lim_(x rarr0)((sqrt(a+x)-sqrt(a))/(x sqrt(a(a+x))))