How to solve this limit?#lim_(x->oo)(xa^(x+1)+1);ain(0,1)#

Question

1898 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-13T14:59:28

#lim_(x to infty)(x a^(x+1)+1)=1#

#lim_(x to infty)(x a^(x+1)+1)#

By rewrititng a bit,

#=lim_(x to infty)(x/(1/a)^(x+1)+1)=lim_(x to infty)(x/(1/a)^(x+1))+1#

By l'H#hat("o")#pital's Rule,

#=lim_(x to infty)1/(ln(1/a)(1/a)^(x+1))+1#

(Note: Since #a in (0,1)# implies that #1/a >1#, #lim_(x to infty)(1/a)^(x+1)=infty#)

#=1/infty+1=0+1=1#

I hope that this was clear.