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-

Question Number 75930 by Rio Michael last updated on 21/Dec/19

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 .