Another Take on how this problem can be interpreted and solved
Break this problem into Numerator and Denominator
That is numerator (10^n + n^20 ) and Denominator is n!
(10^n + n^20 ) is exponential in nature (sum of 2 exponential operands).
The thing to note here is denominator "grows faster" than that of the numerator in this case(factorials grow faster than exponents like example Constant^n or n^constant) .
Hence it starts suppressing the value and as the limit tends to infinity f(x) will tend towards Zero.