How to prove or dis prove ? $if lim_(x->a)f(x)=b and lim_(x->b)g(x)=c$ then $lim_(x->a)g๐f(x)=c$

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Answer 1 · 2017-10-28T08:28:44

See the explanation below

This is the limit of the composition of functions

$lim_(x->a)f(x)=b$

$lim_(x->b)g(x)=c$

Therefore,

$lim_(x->b) go f(x)=g(lim_(x->a)f(x))=c$

because $f(x)$ is approaching $a$ and we are evaluating $g$ at $f(x)$ and this is the same as

$lim_(x->b)g(x)=c$

How to prove or dis prove ? if lim_(x->a)f(x)=b and lim_(x->b)g(x)=cif lim_(x->a)f(x)=b and lim_(x->b)g(x)=c then lim_(x->a)g๐f(x)=clim_(x->a)g๐f(x)=c