consider the function f(x) = { ((1+2x^2 , if x is rational)),((1 + x^4 , if x is irrational)) :} Use the sandwich(pinchin) theorem to prove that lim


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Question Number 75930 by Rio Michael last updated on 21/Dec/19
$consider the function f(x) = { ((1+2x^2 , if x is rational)),((1 + x^4 , if x is irrational)) :} Use the sandwich(pinchin) theorem to prove that lim_(x→0) f(x) = 1.$
$c o n s i d e r t h e f u n c t i o n$ $f (x) = {\begin{cases} 1 + 2 x^{2}, i f x i s r a t i o n a l \\ 1 + x^{4}, i f x i s i r r a t i o n a l \end{cases}$ $U s e t h e s a n d w i c h (p i n c h i n) t h e o r e m t o$ $p r o v e t h a t \lim_{x \to 0} f (x) = 1 .$
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