Question

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`

Answer 1

See the explanation below

Explanation:

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`