Question

find the limit as k approaches infinity of [1+(1/10^k)]^10k

step by step using the l'hospital

Answer 1

we are given

Let's expression as y

now, we can take ln on both sides

now, we can apply L'hospital rule

we can find derivative of top and bottom term

we can apply L'hospital rule again

when we plug k=inf

we get inf/inf

so, we can apply L'hospital rule again

now, we can plug k=inf

now, we can find y

So, we get

............Answer