Given `lim_(x->6) f(x)=3` and `lim_(x->6) g(x)=7` , evaluate `lim_(x->6) sqrt(f(x))`

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tiburtius | High School Teacher | (Level 1) Educator

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Limit and continous function are commutative, that is if `c` is continous at `x_0` then `lim_(x->x_0) c(f(x))=c(lim_(x->x_0) f(x))`. Now since square root is continous at 6 it follows that

`lim_(x->6)sqrt(f(x)) = sqrt(lim_(x->6)f(x)) = sqrt(3)`

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