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

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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.

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