Question

(a) For what values of ( x ) is ( sum_{n=0}^{infty} frac{x^{n}}{n!} ) convergent? ( x geq 0 ) ( x<0 ) for all ( x ) none ( x leq 0 ) (b) What conclusion can be drawn about ( lim _{n ightarrow infty} frac{x^{n}}{n!} ) ? ( lim _{n ightarrow infty} x^{n} / n!=0 ) only for ( x<0 ) ( lim _{n ightarrow infty} x^{n} / n!=0 ) for all values of ( x ) ( lim _{n ightarrow infty} x^{n} / n!=0 ) only for ( x>0 ) No conclusion can be drawn. ( lim _{n ightarrow infty} x^{n} / n!=infty ) for all values of ( x )

          (a) For what values of ( x ) is ( sum_{n=0}^{infty} frac{x^{n}}{n!} ) convergent?
( x geq 0 )
( x<0 )
for all ( x )
none
( x leq 0 )
(b) What conclusion can be drawn about ( lim _{n 
ightarrow infty} frac{x^{n}}{n!} ) ?
( lim _{n 
ightarrow infty} x^{n} / n!=0 ) only for ( x<0 )
( lim _{n 
ightarrow infty} x^{n} / n!=0 ) for all values of ( x )
( lim _{n 
ightarrow infty} x^{n} / n!=0 ) only for ( x>0 )
No conclusion can be drawn.
( lim _{n 
ightarrow infty} x^{n} / n!=infty ) for all values of ( x )

$(a) For what values of ( x ) is ( sumn=0^infty fracx^nn! ) convergent? ( x geq 0 ) ( x<0 ) for all ( x ) none ( x leq 0 ) (b) What conclusion can be drawn about ( lim n ightarrow infty fracx^nn! ) ? ( lim n ightarrow infty x^n / n!=0 ) only for ( x<0 ) ( lim n ightarrow infty x^n / n!=0 ) for all values of ( x ) ( lim n ightarrow infty x^n / n!=0 ) only for ( x>0 ) No conclusion can be drawn. ( lim n ightarrow infty x^n / n!=infty ) for all values of ( x )$

Added by Joel E.

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