The limit of (1+ax)^(1/x) as x approaches infinity is e^a. This conclusion is reached by taking the natural logarithm of the expression, resulting in log(y) = (1/x) log(1+ax). Applying L'Hôpital's Rule leads to the simplification where log(y) approaches 0, confirming that y approaches 1. However, it is crucial to note that the limit is correctly stated as x approaches 0, not infinity.
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Oh! You mean (1+ ax)^(1/x)!abhishek.93 said:Homework Statement
what is limit of (1+ax)^1/x w hen x → ∞ ??
You answer is correct.Homework Equations
answer is e^a
The Attempt at a Solution
taking log i get
log y=1/x log(1+ax)
using l hospital i get
logy=-1/x2 X a/1+ax
so
putting x->∞
we get
logy=0
y=1